Theorems · Definition · group theory
Subsemigroup.carrier
{M : Type u_3} → [inst : Mul M] → Subsemigroup M → Set MThe carrier of a subsemigroup.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Defs
- Cited by
- 160 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Subsemigroupstatement and proof · cited by 323
Cited by270
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
- NonUnitalSubsemiring.centerproof · cited by 22
- Subsemiring.toAddSubmonoidproof · cited by 20
- Submonoid.piproof · cited by 17
- Submonoid.mk.congr_simpstatement and proof · cited by 14
- Subalgebra.starClosureproof · cited by 12
Showing the 200 most cited of 270.