Theorems · Theorem · group theory
SemiconjBy.mul_left
∀ {S : Type u_1} [inst : Semigroup S] {a b x y z : S}, SemiconjBy a y z → SemiconjBy b x y → SemiconjBy (a * b) x zIf b semiconjugates x to y and a semiconjugates y to z, then a * b
semiconjugates x to z.
- Defined in
- Mathlib.Algebra.Group.Semiconj.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_assocproof · cited by 1,667
- Semigroupstatement and proof · cited by 202
- SemiconjBystatement and proof · cited by 99
- SemiconjBy.eqproof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- Commute.mul_leftproof · cited by 5
- IsConj.transproof · cited by 4
- SemiconjBy.isTransproof · cited by 1
- SemiconjBy.natCast_mul_leftproof · cited by 1
- SemiconjBy.intCast_mul_leftproof · cited by 0