Theorems · Definition · group theory
Submonoid.ofClass
{S : Type u_3} → {M : Type u_4} → [inst : Monoid M] → [inst_1 : SetLike S M] → [SubmonoidClass S M] → S → Submonoid MThe actual Submonoid obtained from an element of a SubmonoidClass
- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- MonoidSetLikeSubmonoidClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- SubmonoidClassstatement and proof · cited by 60
Cited by8
Results whose statement or proof uses this declaration.
- RestrictedProduct.unitsEquivstatement and proof · cited by 3
- Submonoid.isUnit_iff_andproof · cited by 2
- Submonoid.inv_mem_of_isUnitproof · cited by 2
- RestrictedProduct.unitsEquiv_applystatement · cited by 0
- RestrictedProduct.mkUnitstatement and proof · cited by 0
- IsDedekindDomain.FiniteAdeleRing.unitsEquiv_finite_valued_eq_onestatement and proof · cited by 0
- RestrictedProduct.coe_unitsEquiv_applystatement · cited by 0
- Submonoid.coe_ofClassstatement and proof · cited by 0