Theorems · Theorem · group theory
addConGen_star
∀ {A : Type u_1} [inst : AddMonoid A] [inst_1 : StarAddMonoid A] {r : A → A → Prop},
(∀ (a b : A), r a b → r (star a) (star b)) → ∀ ⦃a b : A⦄, (addConGen r) a b → (addConGen r) (star a) (star b)- Defined in
- Mathlib.GroupTheory.Congruence.Star
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- AddMonoidStarAddMonoid
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddMonoidstatement and proof · cited by 2,864
- Star.starstatement and proof · cited by 1,082
- StarAddMonoidstatement and proof · cited by 296
- AddConstatement · cited by 138
- addConGenstatement and proof · cited by 28
- AddConGen.Rel.starproof · cited by 1
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