Theorems · Theorem · group theory
FreeGroup.range_map
∀ {α : Type u} {β : Type v} {f : α → β}, (FreeGroup.map f).range = Subgroup.closure (FreeGroup.of '' Set.range f)- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.imagestatement and proof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- MonoidHomproof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.rangestatement and proof · cited by 314
- Set.range_compproof · cited by 223
- Subgroup.closurestatement and proof · cited by 196
- FreeGroupstatement and proof · cited by 132
- FreeGroup.ofstatement and proof · cited by 39
- FreeGroup.mapstatement · cited by 20
- FreeGroup.range_lift_eq_closureproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- FreeGroup.map_surjectiveproof · cited by 1