Theorems · Theorem · group theory
AddMonoidHom.map_exists_right_neg
∀ {M : Type u_4} {N : Type u_5} {F : Type u_9} [inst : AddZero M] [inst_1 : AddZero N] [inst_2 : FunLike F M N]
[AddMonoidHomClass F M N] (f : F) {x : M}, (∃ y, x + y = 0) → ∃ y, f x + y = 0Given an AddMonoid homomorphism f : M →+ N and an element x : M, if x has
a right inverse, then f x has a right inverse too.
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- AddMonoidHomClassstatement and proof · cited by 252
- AddZerostatement and proof · cited by 87
- map_add_eq_zeroproof · cited by 5
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