Theorems · Theorem · ring theory

AlgEquiv.prodCongr_symm_apply

∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_5} {T : Type u_6} {A : Type u_7} {B : Type u_8}
  [inst_1 : Semiring A] [inst_2 : Semiring B] [inst_3 : Semiring S] [inst_4 : Semiring T] [inst_5 : Algebra R S]
  [inst_6 : Algebra R T] [inst_7 : Algebra R A] [inst_8 : Algebra R B] (l : S ≃ₐ[R] A) (r : T ≃ₐ[R] B) (x : A × B),
  (l.prodCongr r).symm x = ((↑l).prodCongr ↑r).symm x

Defined in

Mathlib.Algebra.Algebra.Prod

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebra