Theorems · Theorem · group theory
AddMonoidHom.addCommute_inl_inr
∀ {M : Type u_3} {N : Type u_4} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] (m : M) (n : N),
AddCommute ((AddMonoidHom.inl M N) m) ((AddMonoidHom.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
- AddZeroClassAddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddMonoidHomstatement · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddCommutestatement · cited by 185
- AddMonoidHom.inlstatement · cited by 29
- AddMonoidHom.inrstatement · cited by 29
- AddCommute.zero_rightproof · cited by 6
- AddCommute.zero_leftproof · cited by 5
- AddCommute.prodproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidHom.noncommCoprod_uniquestatement and proof · cited by 1
- AddMonoidHom.noncommCoprod_inl_inrstatement · cited by 0