Freiman.lowerHistory_join_witnesses

Proved

Freiman.lowerHistory_join_witnesses

by tp · Sep 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

hall-raynumber-theory

Finite array indexing combines the disjoint validation batches.

Preamble

import Definitions.Def_Freiman_lowerHistoryVerification
import Mathlib.Tactic

open Freiman

Formal statement

theorem Freiman.lowerHistory_join_witnesses (hs : lowerHistoryPaths.size = 1492 ∧ lowerHistoryWitnesses.size = 1194 ∧ lowerHistoryRecords.size = 3624) (h0 : lowerHistoryWitnessBatch 0 100) (h1 : lowerHistoryWitnessBatch 100 200) (h2 : lowerHistoryWitnessBatch 200 300) (h3 : lowerHistoryWitnessBatch 300 400) (h4 : lowerHistoryWitnessBatch 400 500) (h5 : lowerHistoryWitnessBatch 500 600) (h6 : lowerHistoryWitnessBatch 600 700) (h7 : lowerHistoryWitnessBatch 700 800) (h8 : lowerHistoryWitnessBatch 800 900) (h9 : lowerHistoryWitnessBatch 900 1000) (h10 : lowerHistoryWitnessBatch 1000 1100) (h11 : lowerHistoryWitnessBatch 1100 1194) :
    lowerHistoryAllWitnesses := by
  sorry

Source

Freiman's Hall ray: Proof report and corrected English text (8 September 2026); global_selection.tex, lem:global-suffix-targets; history_certificates.tex, app:all-suffix-histories; verification/families/target_selection/verify_suffix_targets_independent.py; certificates/target_selection/all_suffix_histories_printed.json; role: finite index bookkeeping

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