Theorems · Theorem · group theory
FreeMonoid.mrange_lift
∀ {M : Type u_1} [inst : Monoid M] {α : Type u_4} (f : α → M),
MonoidHom.mrange (FreeMonoid.lift f) = Submonoid.closure (Set.range f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Setproof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.rangestatement and proof · cited by 4,705
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- Set.range_compproof · cited by 223
- Submonoid.mapproof · cited by 190
- Submonoid.closurestatement and proof · cited by 167
- FreeMonoidstatement and proof · cited by 147
- FreeMonoid.ofproof · cited by 69
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.closure_eq_mrangeproof · cited by 3
- Monoid.CoprodI.mrange_eq_iSupproof · cited by 1