Theorems · Inductive type · group theory
SubmonoidClass
(S : Type u_3) → (M : outParam (Type u_4)) → [MulOneClass M] → [SetLike S M] → Prop
SubmonoidClass S M says S is a type of subsets s ≤ M that contain 1
and are closed under (*)
- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- MulOneClassSetLike
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.
- SetLikestatement · cited by 1,084
- MulOneClassstatement · cited by 1,018
Cited by86
Results whose statement or proof uses this declaration.
- MonoidHom.domRestrictstatement and proof · cited by 59
- pow_memstatement and proof · cited by 46
- prod_memstatement and proof · cited by 16
- MonoidHom.domRestrictHomstatement and proof · cited by 12
- SubmonoidClass.subtypestatement and proof · cited by 11
- multiset_prod_memstatement and proof · cited by 11
- IsPrimitiveRoot.coe_submonoidClass_iffstatement and proof · cited by 11
- list_prod_memstatement and proof · cited by 9
- MonoidHom.codRestrictstatement and proof · cited by 8
- MulChar.domRestrictstatement and proof · cited by 8
- Submonoid.ofClassstatement and proof · cited by 6
- SubmonoidClass.coe_powstatement and proof · cited by 5