Theorems · Theorem · group theory
Function.Injective.isMulTorsionFree
∀ {M : Type u_4} {N : Type u_5} [inst : Monoid M] [inst_1 : Monoid N] [IsMulTorsionFree N] (f : M →* N),
Function.Injective ⇑f → IsMulTorsionFree MIf the codomain of an injective monoid homomorphism is torsion free, then so is the domain.
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- MonoidMonoidIsMulTorsionFree
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Cites6
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
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- map_powproof · cited by 503
- IsMulTorsionFreestatement and proof · cited by 44
- IsMulTorsionFree.pow_left_injectiveproof · cited by 2
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