eval — Mathlib

English

For the product prodXSubSMul, evaluating at x yields 0 (follow-up on various isomorphisms).

Русский

Для prodXSubSMul сумма равна 0 при подстановке x.

LaTeX

$$$\text{In particular } (prodXSubSMul\ G\ R\ x).eval x = 0.$$$

Lean4

theorem eval (x : R) : (prodXSubSMul G R x).eval x = 0 :=
  letI := Classical.decEq R
  (map_prod ((Polynomial.aeval x).toRingHom.toMonoidHom : R[X] →* R) _ _).trans <|
    Finset.prod_eq_zero (Finset.mem_univ <| QuotientGroup.mk 1) <| by simp

Похожие утверждения