Theorems · Theorem · group theory
AddConGen.Rel.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.Rel r a b → AddConGen.Rel r (star a) (star b)- Defined in
- Mathlib.GroupTheory.Congruence.Star
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- AddMonoidStarAddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- Star.starstatement and proof · cited by 1,082
- StarAddMonoidstatement and proof · cited by 296
- StarAddMonoid.star_addproof · cited by 29
- AddConGen.Relstatement and proof · cited by 5
- AddConGen.Rel.belowproof · cited by 2
- AddConGen.Rel.brecOnproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- addConGen_starproof · cited by 0