Theorems · Theorem · group theory
FreeGroup.closure_eq_range
∀ {β : Type v} [inst : Group β] (s : Set β), Subgroup.closure s = (FreeGroup.lift Subtype.val).range- 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
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.rangestatement · cited by 314
- Subgroup.closurestatement and proof · cited by 196
- FreeGroupstatement · cited by 132
- Subtype.range_coeproof · cited by 98
- FreeGroup.liftstatement · cited by 32
- FreeGroup.range_lift_eq_closureproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Group.fg_iff_exists_freeGroup_hom_surjectiveproof · cited by 1