Freiman marked initial bridges: chain contacts

Proved

Freiman.lower_bridge_chain_contacts

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

certificatesfreimanlower-construction

Translate exactly the four/three/zero adjacent source contacts to overlap of the prescribed chain.

Preamble

import Definitions.Def_Freiman_lowerBridgeCatalog
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Push

open Freiman

Formal statement

theorem Freiman.lower_bridge_chain_contacts (c : LowerBridgeCase) (n : ℕ) (hc : lowerBridgeZero c = decide (n=0)) (hf : lowerBridgeFamily c ≠ .C) (h : lowerBridgeFacts c n 0) (he : lowerBridgeEndpointFacts c n 0) (ho : ∀ p : LowerPair, lowerEndpoint p false ≤ lowerEndpoint p true) : (lowerBridgeLabels (lowerBridgeFamily c) n).IsChain (fun a b => (lowerCover (lowerPhysicalAdd (lowerFamilyPair (lowerBridgeFamily c) n 0 0) a) ∩ lowerCover (lowerPhysicalAdd (lowerFamilyPair (lowerBridgeFamily c) n 0 0) b)).Nonempty) := by
  sorry

Source

Freiman report, initial_bridges.tex, corrected marked H entries; H_entry_bridges.json 185 exact polynomial records.

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