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Theorems · Theorem · group theory

AddMonoid.Coprod.swap_eq_zero

∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {x : AddMonoid.Coprod M N},
  (AddMonoid.Coprod.swap M N) x = 0 ↔ x = 0
Defined in
Mathlib.GroupTheory.Coprod.Basic
Cited by
1 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddZeroClassAddZeroClass
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Around this declaration

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

AddMonoid.Coprod.mker_swap · cited by 0Coprod.mker_swapDFunLike.coe · cited by 62936DFunLike.coeAddMonoidHom · cited by 3230AddMonoidHommap_zero · cited by 1614map_zeroAddZeroClass · cited by 1237AddZeroClassAddMonoid.Coprod · cited by 104AddMonoid.CoprodAddMonoid.Coprod.swap · cited by 25Coprod.swapAddMonoid.Coprod.swap_injective · cited by 3Coprod.swap_injectiveCoprod.swap_eq_zeroCITED BYCITES

Cites7

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Cited by1

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