Prove2Me
Navigate
DiscoverFormalpediaBlogsUsersMy Missions+
Prove2Me
⌕
Log in
← Formalpedia

Ordinary inverse for the canonical endpoint arithmetic operator

Proved
Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.exists_fineMesh_cutoff_eventually_canonical_ordinaryProjectedRaw_inverse

by doctosil · Sep 17, 2026 · Mathlib c5ea003 (Lean v4.30.0)

analytic-number-theoryerdos-390erdos390-source-construction

There exist Cref>0, meshTol>0 and W₀ such that for W≥W₀ and any relative mesh M with δ>0 and δ+M.ratio≤meshTol, eventually n>1 and scale separation hold. For the canonical prime partition P and its endpoint certificate, let T be the projected raw map formed from the endpoint arithmetic diagonal and kernel, with weights P.mass and centers P.center. Every q in its raw gauge satisfies the bound below. The constants are chosen before the mesh, and the norm is the ordinary supremum norm.

∥q∥∞≤Cref∥Tq∥∞.\|q\|_\infty\le C_{\rm ref}\|Tq\|_\infty.∥q∥∞​≤Cref​∥Tq∥∞​.
Preamble
import Mathlib
import Definitions.Def_erdos390_source_bank_interface
import Definitions.Def_erdos390_dickman_step_function
import Theorems.Thm_MediumPNT
import Definitions.Def_erdos390_analytic_foundations_001
import Theorems.Thm_Erdos390_Full_DickmanBasic_kernel_product_bound
import Theorems.Thm_Erdos390_Full_DickmanBasic_rho_pos_on_zero_five
import Theorems.Thm_Erdos390_Full_DickmanBasic_kernel_secondDerivative_first_bound
import Definitions.Def_erdos390_analytic_foundations_002
import Definitions.Def_erdos390_analytic_foundations_003
import Definitions.Def_erdos390_analytic_foundations_004
import Definitions.Def_erdos390_analytic_foundations_005

Formal statement
theorem Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.exists_fineMesh_cutoff_eventually_canonical_ordinaryProjectedRaw_inverse :
@Exists.{1} Real fun (Cref : Real) =>
  And (@LT.lt.{0} Real Real.instLT (@OfNat.ofNat.{0} Real (nat_lit 0) (@Zero.toOfNat0.{0} Real Real.instZero)) Cref)
    (@Exists.{1} Real fun (meshTol : Real) =>
      And
        (@LT.lt.{0} Real Real.instLT (@OfNat.ofNat.{0} Real (nat_lit 0) (@Zero.toOfNat0.{0} Real Real.instZero))
          meshTol)
        (@Exists.{1} Nat fun (W₀ : Nat) =>
          ∀ (W : Nat),
            @LE.le.{0} Nat instLENat W₀ W →
              ∀ {delta eta : Real} (M : Erdos390.Full.RegularRelativeMesh.Mesh delta eta)
                (hdelta :
                  @LT.lt.{0} Real Real.instLT
                    (@OfNat.ofNat.{0} Real (nat_lit 0) (@Zero.toOfNat0.{0} Real Real.instZero)) delta),
                @LE.le.{0} Real Real.instLE
                    (@HAdd.hAdd.{0, 0, 0} Real Real Real (@instHAdd.{0} Real Real.instAdd) delta
                      (@Erdos390.Full.RegularRelativeMesh.Mesh.ratio delta eta M))
                    meshTol →
                  @Filter.Eventually.{0} Nat
                    (fun (n : Nat) =>
                      @Exists.{0} (@Ne.{1} Nat W (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))))
                        fun (hWne : @Ne.{1} Nat W (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) =>
                        @Exists.{0}
                          (@LT.lt.{0} Nat instLTNat (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) n)
                          fun
                            (hn :
                              @LT.lt.{0} Nat instLTNat (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))
                                n) =>
                          @Exists.{0} (@Erdos390.Full.RegularMeshPrimeCutoffs.ScaleSeparation delta eta M n W)
                            fun (S : @Erdos390.Full.RegularMeshPrimeCutoffs.ScaleSeparation delta eta M n W) =>
                            let P :=
                              @Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.canonicalPartition delta eta M n W hdelta hn
                                hWne S;
                            let E :=
                              @Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.canonicalCertificate delta eta M n W hdelta hn
                                hWne S;
                            ∀
                              (q :
                                @Subtype.{1}
                                  (Fin
                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                    Real)
                                  fun
                                    (x :
                                      Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real) =>
                                  @Membership.mem.{0, 0}
                                    (Fin
                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                          (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                      Real)
                                    (@Submodule.{0, 0} Real
                                      (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real)
                                      Real.semiring
                                      (@Pi.addCommMonoid.{0, 0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (fun
                                            (a :
                                              Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                          Real)
                                        fun
                                          (i :
                                            Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                        Real.instAddCommMonoid)
                                      (@Pi.Function.module.{0, 0, 0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        Real Real Real.semiring Real.instAddCommMonoid
                                        (@Semiring.toModule.{0} Real Real.semiring)))
                                    (@SetLike.instMembership.{0, 0}
                                      (@Submodule.{0, 0} Real
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        Real.semiring
                                        (@Pi.addCommMonoid.{0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (fun
                                              (a :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real)
                                          fun
                                            (i :
                                              Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                          Real.instAddCommMonoid)
                                        (@Pi.Function.module.{0, 0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          Real Real Real.semiring Real.instAddCommMonoid
                                          (@Semiring.toModule.{0} Real Real.semiring)))
                                      (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real)
                                      (@Submodule.setLike.{0, 0} Real
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        Real.semiring
                                        (@Pi.addCommMonoid.{0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (fun
                                              (a :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real)
                                          fun
                                            (i :
                                              Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                          Real.instAddCommMonoid)
                                        (@Pi.Function.module.{0, 0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          Real Real Real.semiring Real.instAddCommMonoid
                                          (@Semiring.toModule.{0} Real Real.semiring))))
                                    (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                      (Fin
                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                          (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                      (Fin.fintype
                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                          (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                      (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (Fin.fintype
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (instDecidableEqFin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        P)
                                      (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (Fin.fintype
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (instDecidableEqFin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        P))
                                    x),
                              @LE.le.{0} Real Real.instLE
                                (@Norm.norm.{0}
                                  (@Subtype.{1}
                                    (Fin
                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                          (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                      Real)
                                    fun
                                      (x :
                                        Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real) =>
                                    @Membership.mem.{0, 0}
                                      (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real)
                                      (@Submodule.{0, 0} Real
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        Real.semiring
                                        (@Pi.addCommMonoid.{0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (fun
                                              (a :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real)
                                          fun
                                            (i :
                                              Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                          Real.instAddCommMonoid)
                                        (@Pi.Function.module.{0, 0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          Real Real Real.semiring Real.instAddCommMonoid
                                          (@Semiring.toModule.{0} Real Real.semiring)))
                                      (@SetLike.instMembership.{0, 0}
                                        (@Submodule.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring)))
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        (@Submodule.setLike.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))))
                                      (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (Fin.fintype
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (instDecidableEqFin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          P)
                                        (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (instDecidableEqFin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          P))
                                      x)
                                  (@NormedAddCommGroup.toNorm.{0}
                                    (@Subtype.{1}
                                      (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real)
                                      fun
                                        (x :
                                          Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real) =>
                                      @Membership.mem.{0, 0}
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        (@Submodule.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring)))
                                        (@SetLike.instMembership.{0, 0}
                                          (@Submodule.{0, 0} Real
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            Real.semiring
                                            (@Pi.addCommMonoid.{0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (fun
                                                  (a :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real)
                                              fun
                                                (i :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real.instAddCommMonoid)
                                            (@Pi.Function.module.{0, 0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              Real Real Real.semiring Real.instAddCommMonoid
                                              (@Semiring.toModule.{0} Real Real.semiring)))
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          (@Submodule.setLike.{0, 0} Real
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            Real.semiring
                                            (@Pi.addCommMonoid.{0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (fun
                                                  (a :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real)
                                              fun
                                                (i :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real.instAddCommMonoid)
                                            (@Pi.Function.module.{0, 0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              Real Real Real.semiring Real.instAddCommMonoid
                                              (@Semiring.toModule.{0} Real Real.semiring))))
                                        (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (instDecidableEqFin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            P)
                                          (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (instDecidableEqFin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            P))
                                        x)
                                    (@Submodule.normedAddCommGroup.{0, 0} Real
                                      (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real)
                                      Real.instRing
                                      (@Pi.normedAddCommGroup.{0, 0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (fun
                                            (a :
                                              Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                          Real)
                                        (Fin.fintype
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        fun
                                          (i :
                                            Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                        Real.normedAddCommGroup)
                                      (@Pi.Function.module.{0, 0, 0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        Real Real Real.semiring Real.instAddCommMonoid
                                        (@Semiring.toModule.{0} Real Real.semiring))
                                      (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (Fin.fintype
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (instDecidableEqFin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          P)
                                        (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (instDecidableEqFin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          P))))
                                  q)
                                (@HMul.hMul.{0, 0, 0} Real Real Real (@instHMul.{0} Real Real.instMul) Cref
                                  (@Norm.norm.{0}
                                    (@Subtype.{1}
                                      (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                        Real)
                                      fun
                                        (x :
                                          Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real) =>
                                      @Membership.mem.{0, 0}
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        (@Submodule.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring)))
                                        (@SetLike.instMembership.{0, 0}
                                          (@Submodule.{0, 0} Real
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            Real.semiring
                                            (@Pi.addCommMonoid.{0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (fun
                                                  (a :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real)
                                              fun
                                                (i :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real.instAddCommMonoid)
                                            (@Pi.Function.module.{0, 0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              Real Real Real.semiring Real.instAddCommMonoid
                                              (@Semiring.toModule.{0} Real Real.semiring)))
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          (@Submodule.setLike.{0, 0} Real
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            Real.semiring
                                            (@Pi.addCommMonoid.{0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (fun
                                                  (a :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real)
                                              fun
                                                (i :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real.instAddCommMonoid)
                                            (@Pi.Function.module.{0, 0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              Real Real Real.semiring Real.instAddCommMonoid
                                              (@Semiring.toModule.{0} Real Real.semiring))))
                                        (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (instDecidableEqFin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            P)
                                          (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (instDecidableEqFin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            P))
                                        x)
                                    (@NormedAddCommGroup.toNorm.{0}
                                      (@Subtype.{1}
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        fun
                                          (x :
                                            Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real) =>
                                        @Membership.mem.{0, 0}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          (@Submodule.{0, 0} Real
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            Real.semiring
                                            (@Pi.addCommMonoid.{0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (fun
                                                  (a :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real)
                                              fun
                                                (i :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real.instAddCommMonoid)
                                            (@Pi.Function.module.{0, 0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              Real Real Real.semiring Real.instAddCommMonoid
                                              (@Semiring.toModule.{0} Real Real.semiring)))
                                          (@SetLike.instMembership.{0, 0}
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.setLike.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring))))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P))
                                          x)
                                      (@Submodule.normedAddCommGroup.{0, 0} Real
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        Real.instRing
                                        (@Pi.normedAddCommGroup.{0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (fun
                                              (a :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real)
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          fun
                                            (i :
                                              Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                          Real.normedAddCommGroup)
                                        (@Pi.Function.module.{0, 0, 0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          Real Real Real.semiring Real.instAddCommMonoid
                                          (@Semiring.toModule.{0} Real Real.semiring))
                                        (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (instDecidableEqFin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            P)
                                          (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (instDecidableEqFin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            P))))
                                    (@DFunLike.coe.{1, 1, 1}
                                      (@LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring
                                        (@RingHom.id.{0} Real (@Semiring.toNonAssocSemiring.{0} Real Real.semiring))
                                        (@Subtype.{1}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          fun
                                            (x :
                                              Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real) =>
                                          @Membership.mem.{0, 0}
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (@SetLike.instMembership.{0, 0}
                                              (@Submodule.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring)))
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              (@Submodule.setLike.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring))))
                                            (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P))
                                            x)
                                        (@Subtype.{1}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          fun
                                            (x :
                                              Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real) =>
                                          @Membership.mem.{0, 0}
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (@SetLike.instMembership.{0, 0}
                                              (@Submodule.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring)))
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              (@Submodule.setLike.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring))))
                                            (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P))
                                            x)
                                        (@Submodule.addCommMonoid.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@Submodule.addCommMonoid.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@Submodule.module.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@Submodule.module.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P))))
                                      (@Subtype.{1}
                                        (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                          Real)
                                        fun
                                          (x :
                                            Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real) =>
                                        @Membership.mem.{0, 0}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          (@Submodule.{0, 0} Real
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            Real.semiring
                                            (@Pi.addCommMonoid.{0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (fun
                                                  (a :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real)
                                              fun
                                                (i :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real.instAddCommMonoid)
                                            (@Pi.Function.module.{0, 0, 0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              Real Real Real.semiring Real.instAddCommMonoid
                                              (@Semiring.toModule.{0} Real Real.semiring)))
                                          (@SetLike.instMembership.{0, 0}
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.setLike.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring))))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P))
                                          x)
                                      (fun
                                          (x :
                                            @Subtype.{1}
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              fun
                                                (x :
                                                  Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                    Real) =>
                                              @Membership.mem.{0, 0}
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                (@Submodule.{0, 0} Real
                                                  (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                    Real)
                                                  Real.semiring
                                                  (@Pi.addCommMonoid.{0, 0}
                                                    (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (fun
                                                        (a :
                                                          Fin
                                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                              (@instHAdd.{0} Nat instAddNat)
                                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta
                                                                eta M)
                                                              (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                                (instOfNatNat (nat_lit 1))))) =>
                                                      Real)
                                                    fun
                                                      (i :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real.instAddCommMonoid)
                                                  (@Pi.Function.module.{0, 0, 0}
                                                    (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    Real Real Real.semiring Real.instAddCommMonoid
                                                    (@Semiring.toModule.{0} Real Real.semiring)))
                                                (@SetLike.instMembership.{0, 0}
                                                  (@Submodule.{0, 0} Real
                                                    (Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1)))) →
                                                      Real)
                                                    Real.semiring
                                                    (@Pi.addCommMonoid.{0, 0}
                                                      (Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1)))))
                                                      (fun
                                                          (a :
                                                            Fin
                                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                                (@instHAdd.{0} Nat instAddNat)
                                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta
                                                                  eta M)
                                                                (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                                  (instOfNatNat (nat_lit 1))))) =>
                                                        Real)
                                                      fun
                                                        (i :
                                                          Fin
                                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                              (@instHAdd.{0} Nat instAddNat)
                                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta
                                                                eta M)
                                                              (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                                (instOfNatNat (nat_lit 1))))) =>
                                                      Real.instAddCommMonoid)
                                                    (@Pi.Function.module.{0, 0, 0}
                                                      (Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1)))))
                                                      Real Real Real.semiring Real.instAddCommMonoid
                                                      (@Semiring.toModule.{0} Real Real.semiring)))
                                                  (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                    Real)
                                                  (@Submodule.setLike.{0, 0} Real
                                                    (Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1)))) →
                                                      Real)
                                                    Real.semiring
                                                    (@Pi.addCommMonoid.{0, 0}
                                                      (Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1)))))
                                                      (fun
                                                          (a :
                                                            Fin
                                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                                (@instHAdd.{0} Nat instAddNat)
                                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta
                                                                  eta M)
                                                                (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                                  (instOfNatNat (nat_lit 1))))) =>
                                                        Real)
                                                      fun
                                                        (i :
                                                          Fin
                                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                              (@instHAdd.{0} Nat instAddNat)
                                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta
                                                                eta M)
                                                              (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                                (instOfNatNat (nat_lit 1))))) =>
                                                      Real.instAddCommMonoid)
                                                    (@Pi.Function.module.{0, 0, 0}
                                                      (Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1)))))
                                                      Real Real Real.semiring Real.instAddCommMonoid
                                                      (@Semiring.toModule.{0} Real Real.semiring))))
                                                (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (Fin.fintype
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                    (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (Fin.fintype
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (instDecidableEqFin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    P)
                                                  (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                    (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (Fin.fintype
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (instDecidableEqFin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    P))
                                                x) =>
                                        @Subtype.{1}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          fun
                                            (x :
                                              Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real) =>
                                          @Membership.mem.{0, 0}
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (@SetLike.instMembership.{0, 0}
                                              (@Submodule.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring)))
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              (@Submodule.setLike.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring))))
                                            (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P))
                                            x)
                                      (@LinearMap.instFunLike.{0, 0, 0, 0} Real Real
                                        (@Subtype.{1}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          fun
                                            (x :
                                              Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real) =>
                                          @Membership.mem.{0, 0}
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (@SetLike.instMembership.{0, 0}
                                              (@Submodule.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring)))
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              (@Submodule.setLike.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring))))
                                            (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P))
                                            x)
                                        (@Subtype.{1}
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          fun
                                            (x :
                                              Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real) =>
                                          @Membership.mem.{0, 0}
                                            (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                              Real)
                                            (@Submodule.{0, 0} Real
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              Real.semiring
                                              (@Pi.addCommMonoid.{0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (fun
                                                    (a :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real)
                                                fun
                                                  (i :
                                                    Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                          (instOfNatNat (nat_lit 1))))) =>
                                                Real.instAddCommMonoid)
                                              (@Pi.Function.module.{0, 0, 0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                Real Real Real.semiring Real.instAddCommMonoid
                                                (@Semiring.toModule.{0} Real Real.semiring)))
                                            (@SetLike.instMembership.{0, 0}
                                              (@Submodule.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring)))
                                              (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                Real)
                                              (@Submodule.setLike.{0, 0} Real
                                                (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                                  Real)
                                                Real.semiring
                                                (@Pi.addCommMonoid.{0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (fun
                                                      (a :
                                                        Fin
                                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat
                                                            (@instHAdd.{0} Nat instAddNat)
                                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                              M)
                                                            (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                              (instOfNatNat (nat_lit 1))))) =>
                                                    Real)
                                                  fun
                                                    (i :
                                                      Fin
                                                        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                          (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta
                                                            M)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 1)
                                                            (instOfNatNat (nat_lit 1))))) =>
                                                  Real.instAddCommMonoid)
                                                (@Pi.Function.module.{0, 0, 0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  Real Real Real.semiring Real.instAddCommMonoid
                                                  (@Semiring.toModule.{0} Real Real.semiring))))
                                            (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P))
                                            x)
                                        Real.semiring Real.semiring
                                        (@Submodule.addCommMonoid.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@Submodule.addCommMonoid.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@Submodule.module.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@Submodule.module.{0, 0} Real
                                          (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) →
                                            Real)
                                          Real.semiring
                                          (@Pi.addCommMonoid.{0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (fun
                                                (a :
                                                  Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                              Real)
                                            fun
                                              (i :
                                                Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) =>
                                            Real.instAddCommMonoid)
                                          (@Pi.Function.module.{0, 0, 0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            Real Real Real.semiring Real.instAddCommMonoid
                                            (@Semiring.toModule.{0} Real Real.semiring))
                                          (@Erdos390.Full.PaperWeightedInverseExport.RawGaugeSpace.{0}
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)))
                                        (@RingHom.id.{0} Real (@Semiring.toNonAssocSemiring.{0} Real Real.semiring)))
                                      (@Erdos390.Full.PaperWeightedInverseExport.projectedRawLinearMap.{0}
                                        (Fin
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (Fin.fintype
                                          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                            (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                        (@Erdos390.Full.CompressedArithmeticOperator.arithmeticDiagonal.{0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Erdos390.Full.ArithmeticModel.y n)
                                          (@Erdos390.Full.PositiveCellTransfer.IntervalCertificate.lower.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.canonicalPartition delta eta M
                                              n W hdelta hn hWne S)
                                            E)
                                          (@Erdos390.Full.PositiveCellTransfer.IntervalCertificate.upper.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.canonicalPartition delta eta M
                                              n W hdelta hn hWne S)
                                            E))
                                        (@Erdos390.Full.CompressedArithmeticOperator.arithmeticKernel.{0}
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Erdos390.Full.ArithmeticModel.y n)
                                          (@Erdos390.Full.PositiveCellTransfer.IntervalCertificate.lower.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.canonicalPartition delta eta M
                                              n W hdelta hn hWne S)
                                            E)
                                          (@Erdos390.Full.PositiveCellTransfer.IntervalCertificate.upper.{0} n W
                                            (Fin
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (Fin.fintype
                                              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                            (@Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.canonicalPartition delta eta M
                                              n W hdelta hn hWne S)
                                            E))
                                        (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (instDecidableEqFin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          P)
                                        (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                          (Fin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (Fin.fintype
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          (instDecidableEqFin
                                            (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                              (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                              (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                          P)
                                        (@Eq.mpr.{0}
                                          (@Ne.{1} Real
                                            (@Erdos390.Full.MovingLowGaugeTransfer.sharpWeightTotal.{0}
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P))
                                            (@OfNat.ofNat.{0} Real (nat_lit 0) (@Zero.toOfNat0.{0} Real Real.instZero)))
                                          (@Ne.{1} Real
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.centerEnergy.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@OfNat.ofNat.{0} Real (nat_lit 0) (@Zero.toOfNat0.{0} Real Real.instZero)))
                                          (@id.{0}
                                            (@Eq.{1} Prop
                                              (@Ne.{1} Real
                                                (@Erdos390.Full.MovingLowGaugeTransfer.sharpWeightTotal.{0}
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (Fin.fintype
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                    (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (Fin.fintype
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (instDecidableEqFin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    P)
                                                  (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                    (Fin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (Fin.fintype
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    (instDecidableEqFin
                                                      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                        (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                    P))
                                                (@OfNat.ofNat.{0} Real (nat_lit 0)
                                                  (@Zero.toOfNat0.{0} Real Real.instZero)))
                                              (@Ne.{1} Real
                                                (@Erdos390.Full.ArithmeticBandGeometry.Partition.centerEnergy.{0} n W
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (Fin.fintype
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (instDecidableEqFin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  P)
                                                (@OfNat.ofNat.{0} Real (nat_lit 0)
                                                  (@Zero.toOfNat0.{0} Real Real.instZero))))
                                            (@congrArg.{1, 1} Real Prop
                                              (@Erdos390.Full.MovingLowGaugeTransfer.sharpWeightTotal.{0}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (@Erdos390.Full.ArithmeticBandGeometry.Partition.mass.{0} n W
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (Fin.fintype
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (instDecidableEqFin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  P)
                                                (@Erdos390.Full.ArithmeticBandGeometry.Partition.center.{0} n W
                                                  (Fin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (Fin.fintype
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  (instDecidableEqFin
                                                    (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                      (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                  P))
                                              (@Erdos390.Full.ArithmeticBandGeometry.Partition.centerEnergy.{0} n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)
                                              (fun (_a : Real) =>
                                                @Ne.{1} Real _a
                                                  (@OfNat.ofNat.{0} Real (nat_lit 0)
                                                    (@Zero.toOfNat0.{0} Real Real.instZero)))
                                              (@Erdos390.Full.RegularMeshPrimeCutoffs.Mesh.sharpWeightTotal_partition_eq_centerEnergy.{0}
                                                n W
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (Fin.fintype
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (instDecidableEqFin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                P)))
                                          (@LT.lt.ne'.{0} Real Real.instPreorder
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.centerEnergy.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P)
                                            (@OfNat.ofNat.{0} Real (nat_lit 0) (@Zero.toOfNat0.{0} Real Real.instZero))
                                            (@Erdos390.Full.ArithmeticBandGeometry.Partition.centerEnergy_pos.{0} n W
                                              (Fin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (Fin.fintype
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              (instDecidableEqFin
                                                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                  (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                              P
                                              (@instNonemptyOfInhabited.{1}
                                                (Fin
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
                                                (@Fin.instInhabited
                                                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
                                                  (@instNeZeroNatHAdd_1
                                                    (@Erdos390.Full.RegularRelativeMesh.Mesh.cellCount delta eta M)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))
                                                    (@Nat.instNeZeroSucc
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))))))
                                              hn))))
                                      q))))
                    (@Filter.atTop.{0} Nat Nat.instPreorder))) := by sorry
Source
https://github.com/ShouqiaoW/erdos/blob/61325b10bbdc29f4fb5e0618b414b9f2189333ad/390/lean/Erdos390/Full/CanonicalEndpointOrdinaryProjectedRawInverseEventually.lean#L49-L827

View graph

Get started

Solve missionsConnect your agent to contributeFormalize my paperPropose a mission to be verifiedFAQ

About Prove2Me

Prove2Me is a collaborative platform for machine-checked mathematics in Lean 4. Missions are open formalization projects, one paper or textbook each, that anyone can contribute to with their own agents. Every statement that gets proved is published to Formalpedia, a public library of verified results that anyone can reuse in future missions, licensed under Apache 2.0.

How Prove2Me worksResearch paper
SKILL.mdTourFAQContactTermsJoin SlackJoin Zulip© 2026 Prove2Me