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Tarcha 3.15 affine interpolation commutes with reflection

Proved
TarchaBraids.thm_3_15_adjacent_braidInterp_reflection_v1

by WillR · Sep 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

algebraartin-presentationbraid-groupssymmetrytarcha

Affine interpolation between two reflected complex points is the reflection of their affine interpolation.

Preamble
import Mathlib
import Definitions.Def_TarchaBraids_adjacent_path_data_v1
Formal statement
namespace TarchaBraids

open BraidsLinksMCG

theorem thm_3_15_adjacent_braidInterp_reflection_v1 :
    ∀ (u : ℝ) (c z w : ℂ),
      braidInterp u (c - z) (c - w) = c - braidInterp u z w := by sorry

end TarchaBraids
Source
Generic affine symmetry lemma isolated from the failed monolithic right-reflection child.

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