Theorems · Theorem · group theory
FreeGroup.closure_range_of
∀ (α : Type u_1), Subgroup.closure (Set.range FreeGroup.of) = ⊤
The generators of FreeGroup α generate FreeGroup α. That is, the subgroup closure of the
set of generators equals ⊤.
- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 2 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Set.rangestatement · cited by 4,705
- MonoidHomproof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.rangeproof · cited by 314
- Subgroup.closurestatement · cited by 196
- FreeGroupstatement and proof · cited by 132
- FreeGroup.ofstatement · cited by 39
- MonoidHom.range_eq_topproof · cited by 29
- FreeGroup.range_lift_eq_closureproof · cited by 5
- FreeGroup.lift_of_eq_idproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- FreeGroup.map_surjectiveproof · cited by 1
- PresentedGroup.closure_range_ofproof · cited by 1