Theorems · Inductive type · group theory
Subsemigroup
(M : Type u_3) → [Mul M] → Type u_3
A subsemigroup of a magma M is a subset closed under multiplication.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Defs
- Cited by
- 323 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by408
Results whose statement or proof uses this declaration.
- Subsemigroup.carrierstatement and proof · cited by 160
- Submonoid.toSubsemigroupstatement · cited by 159
- Subsemigroup.mapstatement and proof · cited by 51
- Subsemigroup.closurestatement and proof · cited by 43
- Subsemigroup.comapstatement and proof · cited by 39
- Subsemigroup.centerstatement · cited by 38
- Subsemigroup.opstatement and proof · cited by 28
- Subsemigroup.unopstatement and proof · cited by 25
- NonUnitalSubsemiring.mapproof · cited by 22
- NonUnitalSubsemiring.centerproof · cited by 22
- NonUnitalSubring.mapproof · cited by 19
- Subsemigroup.opEquivstatement and proof · cited by 18
Showing the 200 most cited of 408.