mk_quotientEquivOfIsCompl_apply — Mathlib

English

The symm application of quotientEquivOfIsCompl to mk x yields x in the quotient; i.e., the simplification lemma for mk_coe holds.

Русский

Симм применение quotientEquivOfIsCompl к mk x возвращает x в декомпозируемом виде; лемма mk_coe справедлива.

LaTeX

$$$quotientEquivOfIsCompl p q h (Quotient.mk x) = x$$$

Lean4

@[simp]
theorem mk_quotientEquivOfIsCompl_apply (h : IsCompl p q) (x : E ⧸ p) :
    (Quotient.mk (quotientEquivOfIsCompl p q h x) : E ⧸ p) = x :=
  (quotientEquivOfIsCompl p q h).symm_apply_apply x

Похожие утверждения