Theorems · Theorem · group theory
IsIdempotentElem.mul_of_commute
∀ {S : Type u_3} [inst : Semigroup S] {a b : S},
Commute a b → IsIdempotentElem a → IsIdempotentElem b → IsIdempotentElem (a * b)- Defined in
- Mathlib.Algebra.Group.Idempotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Commutestatement and proof · cited by 639
- IsIdempotentElemstatement and proof · cited by 217
- Semigroupstatement and proof · cited by 202
- Commute.symmproof · cited by 79
- IsIdempotentElem.eqproof · cited by 42
- Commute.mul_mul_mul_commproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- IsIdempotentElem.mulproof · cited by 3
- IsLprojection.mulproof · cited by 1
- IsStarProjection.mulproof · cited by 0