Theorems · Theorem · group theory
FreeGroup.map_injective
∀ {α : Type u} {β : Type v} {f : α → β}, Function.Injective f → Function.Injective ⇑(FreeGroup.map f)If α and β are arbitrary types and there is an injection between them,
then the induced map on their free groups is also injective.
- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- MonoidHomstatement · cited by 3,629
- IsEmptyproof · cited by 759
- FreeGroupstatement and proof · cited by 132
- Function.invFunproof · cited by 60
- FreeGroup.mapstatement and proof · cited by 20
- Function.injective_of_subsingletonproof · cited by 17
- Function.injective_iff_hasLeftInverseproof · cited by 5
- FreeGroup.map.idproof · cited by 3
- Function.invFun_compproof · cited by 2
- FreeGroup.map.compproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- FreeGroup.map_bijectiveproof · cited by 0