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Theorems · Theorem · group theory

AddMonoid.Coprod.lift_swap

∀ {M : Type u_1} {N : Type u_2} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] [inst_2 : AddMonoid P]
  (f : M →+ P) (g : N →+ P) (x : AddMonoid.Coprod N M),
  (AddMonoid.Coprod.lift f g) ((AddMonoid.Coprod.swap N M) x) = (AddMonoid.Coprod.lift g f) 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
AddZeroClassAddZeroClassAddMonoid
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Around this declaration

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

AddMonoid.Coprod.fst_swap · cited by 0Coprod.fst_swapAddMonoid.Coprod.snd_swap · cited by 0Coprod.snd_swapDFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidAddZeroClass · cited by 1237AddZeroClassDFunLike.congr_fun · cited by 288DFunLike.congr_funAddMonoid.Coprod · cited by 104AddMonoid.CoprodAddMonoid.Coprod.swap · cited by 25Coprod.swapAddMonoid.Coprod.lift · cited by 13Coprod.liftAddMonoid.Coprod.lift_comp_swap · cited by 3Coprod.lift_comp_swapCoprod.lift_swapCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.