congr_symm — Mathlib

English

Congruence is multiplicative in both arguments: congr (f1 * f2) (g1 * g2) = congr f1 g1 * congr f2 g2.

Русский

Конгруэнтность мультипликативна в обоих аргументах: congr (f1 * f2) (g1 * g2) = congr f1 g1 * congr f2 g2.

LaTeX

$$$\mathrm{congr\_mul} : \mathrm{congr}(f_1 f_2, g_1 g_2) = \mathrm{congr}(f_1,g_1) \; \mathrm{congr}(f_2,g_2)$$$

Lean4

theorem congr_symm (f : M ≃ₗ[A] P) (g : N ≃ₗ[R] Q) : congr f.symm g.symm = (congr f g).symm :=
  rfl

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