neg_one_pow_smul_map_insertNth — Mathlib

English

DomCoprod' applied to a simple tensor equals DomCoprod.

Русский

DomCoprod' при применении к простому тензору равен DomCoprod.

LaTeX

$$$$ domCoprod'(a \otimes_{R'} b) = domCoprod(a,b). $$$$

Lean4

theorem neg_one_pow_smul_map_insertNth (f : M [⋀^Fin (n + 1)]→ₗ[R] N) (p : Fin (n + 1)) (x : M) (v : Fin n → M) :
    (-1) ^ (p : ℕ) • f (p.insertNth x v) = f (Matrix.vecCons x v) :=
  by
  rw [map_insertNth, smul_smul, ← pow_add, Even.neg_one_pow, one_smul]
  use p

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