Mathlib Map

Theorems · Theorem · group theory

AddMonoid.Coprod.swap_swap

∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] (x : AddMonoid.Coprod M N),
  (AddMonoid.Coprod.swap N M) ((AddMonoid.Coprod.swap M N) x) = x
Defined in
Mathlib.GroupTheory.Coprod.Basic
Cited by
2 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddZeroClassAddZeroClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddMonoid.Coprod.swap_injective · cited by 3Coprod.swap_injectiveAddMonoid.Coprod.swap_surjective · cited by 3Coprod.swap_surjectiveDFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassDFunLike.congr_fun · cited by 288DFunLike.congr_funAddMonoid.Coprod · cited by 104AddMonoid.CoprodAddMonoid.Coprod.swap · cited by 25Coprod.swapAddMonoid.Coprod.swap_comp_swap · cited by 1Coprod.swap_comp_swapCoprod.swap_swapCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.