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Theorems · Theorem · group theory

MonoidHom.commute_inl_inr

∀ {M : Type u_3} {N : Type u_4} [inst : MulOneClass M] [inst_1 : MulOneClass N] (m : M) (n : N),
  Commute ((MonoidHom.inl M N) m) ((MonoidHom.inr M N) n)
Defined in
Mathlib.Algebra.Group.Prod
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
MulOneClassMulOneClass
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Around this declaration

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

MonoidHom.noncommCoprod_unique · cited by 1MonoidHom.noncommCoprod_u…MonoidHom.noncommCoprod_inl_inr · cited by 0MonoidHom.noncommCoprod_i…DFunLike.coe · cited by 62936DFunLike.coeMonoidHom · cited by 3629MonoidHomMulOneClass · cited by 1018MulOneClassCommute · cited by 639CommuteMonoidHom.inl · cited by 32MonoidHom.inlMonoidHom.inr · cited by 32MonoidHom.inrCommute.one_right · cited by 22Commute.one_rightCommute.one_left · cited by 15Commute.one_leftCommute.prod · cited by 3Commute.prodMonoidHom.commute_inl_inrCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.