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Theorems · Theorem · group theory

SemiconjBy.isTrans

∀ {S : Type u_1} [inst : Semigroup S], IsTrans S fun a b => ∃ c, SemiconjBy c a b

The relation “there exists an element that semiconjugates a to b” on a semigroup is transitive.

Defined in
Mathlib.Algebra.Group.Semiconj.Defs
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
Semigroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SemiconjBy.transitive · cited by 0SemiconjBy.transitiveSemigroup · cited by 202SemigroupIsTrans · cited by 157IsTransSemiconjBy · cited by 99SemiconjBySemiconjBy.mul_left · cited by 5SemiconjBy.mul_leftSemiconjBy.isTransCITED BYCITES

Cites4

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Cited by1

Results whose statement or proof uses this declaration.