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Theorems · Theorem · group theory

Monoid.Coprod.swap_swap

∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] (x : Monoid.Coprod M N),
  (Monoid.Coprod.swap N M) ((Monoid.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
MulOneClassMulOneClass
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Around this declaration

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

Monoid.Coprod.swap_surjective · cited by 3Coprod.swap_surjectiveMonoid.Coprod.swap_injective · cited by 3Coprod.swap_injectiveDFunLike.coe · cited by 62936DFunLike.coeMonoidHom · cited by 3629MonoidHomMulOneClass · cited by 1018MulOneClassDFunLike.congr_fun · cited by 288DFunLike.congr_funMonoid.Coprod · cited by 109Monoid.CoprodMonoid.Coprod.swap · cited by 25Coprod.swapMonoid.Coprod.swap_comp_swap · cited by 1Coprod.swap_comp_swapCoprod.swap_swapCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.