Tarcha 3.15 right interpolation injectivity

Proved

TarchaBraids.thm_3_15_adjacent_right_interp_injective_v1

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

artin-presentationbraid-groupsconfiguration-spaceinjectivitytarcha

For interpolation and path parameters in the unit interval, the right interpolation map is injective on strand indices.

Preamble

import Mathlib
import Definitions.Def_TarchaBraids_adjacent_path_data_v1
import Theorems.Thm_TarchaBraids_thm_3_15_adjacent_outer_outside_facts_v1
import Theorems.Thm_TarchaBraids_thm_3_15_adjacent_right_pairwise_separation_v1
import Theorems.Thm_TarchaBraids_thm_3_15_adjacent_right_outside_separation_v1

Formal statement

namespace TarchaBraids

open BraidsLinksMCG

theorem thm_3_15_adjacent_right_interp_injective_v1 :
    ∀ {n : ℕ} (i j : Fin (n - 1)) (hji : (j : ℕ) = (i : ℕ) + 1)
      (u q : ℝ), 0 ≤ u → u ≤ 1 → 0 ≤ q → q ≤ 1 →
      Function.Injective (rightOuterInterpFun n i j u q) := by sorry

end TarchaBraids

Source

Case split assembled from modular right pairwise and right distinguished-to-outside separation theorems.

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