Theorems · Theorem · group theory
FreeGroup.lift_surjective_iff_closure_range_eq_top
∀ {α : Type u} {β : Type v} [inst : Group β] {f : α → β},
Function.Surjective ⇑(FreeGroup.lift f) ↔ Subgroup.closure (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
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Top.topstatement and proof · cited by 9,680
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- Set.rangestatement and proof · cited by 4,705
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.closurestatement and proof · cited by 196
- FreeGroupstatement · cited by 132
- FreeGroup.liftstatement · cited by 32
- MonoidHom.range_eq_topproof · cited by 29
- FreeGroup.range_lift_eq_closureproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Group.Generators.lift_val_surjectiveproof · cited by 1