Theorems · Definition · group theory
Submonoid.toSubsemigroup
{M : Type u_3} → [inst : MulOneClass M] → Submonoid M → Subsemigroup MA submonoid of a monoid M can be considered as a subsemigroup of that monoid.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 159 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Subsemigroupstatement · cited by 323
Cited by257
Results whose statement or proof uses this declaration.
- fixingSubgroupproof · cited by 83
- IntermediateField.restrictScalarsproof · cited by 66
- Subsemiring.opproof · cited by 43
- StarAlgebra.adjoinproof · cited by 42
- Subring.mapproof · cited by 33
- Subsemiring.unopproof · cited by 26
- Subring.comapproof · cited by 22
- Subsemiring.toAddSubmonoidproof · cited by 20
- Submonoid.piproof · cited by 17
- Subalgebra.starClosureproof · cited by 12
- Subring.toAddSubgroupproof · cited by 11
- Subalgebra.toNonUnitalSubalgebraproof · cited by 11
Showing the 200 most cited of 257.