Theorems · Theorem · group theory
PresentedMonoid.closure_range_of
∀ {α : Type u_2} (rels : FreeMonoid α → FreeMonoid α → Prop),
Submonoid.closure (Set.range (PresentedMonoid.of rels)) = ⊤The generators of a presented monoid generate the presented monoid. That is, the submonoid
closure of the set of generators equals ⊤.
- Defined in
- Mathlib.Algebra.PresentedMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topstatement · cited by 9,680
- Set.rangestatement and proof · cited by 4,705
- Submonoidstatement · cited by 3,086
- Submonoid.closurestatement and proof · cited by 167
- FreeMonoidstatement and proof · cited by 147
- FreeMonoid.ofproof · cited by 69
- Submonoid.subset_closureproof · cited by 46
- Submonoid.mul_memproof · cited by 33
- Submonoid.one_memproof · cited by 28
- PresentedMonoidstatement and proof · cited by 10
- PresentedMonoid.mkproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- PresentedMonoid.extproof · cited by 1