`BookProof.SmCar.jwSign_insert` {i j : Fin n} {S : Finset (Fin n)} (hj : j ∉ S) : jwSign i (insert j S) = (if j < i then -1 else 1) * jwSign i S

Proved

BookProof.SmCar.jwSign_insert

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.jwSign_insert {i j : Fin n} {S : Finset (Fin n)} (hj : j ∉ S) : jwSign i (insert j S) = (if j < i then -1 else 1) * jwSign i S

Formalization note: Lean 4 identifier BookProof.SmCar.jwSign_insert.

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.jwSign_insert
import Mathlib
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.jwSign_insert {i j : Fin n} {S : Finset (Fin n)} (hj : j ∉ S) :
    jwSign i (insert j S) = (if j < i then -1 else 1) * jwSign i S := by sorry

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