Mathlib Map

Theorems · Theorem

Function.Semiconj.trans

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {fab : α → β} {fbc : β → γ} {ga : α → α} {gb : β → β} {gc : γ → γ},
  Function.Semiconj fab ga gb → Function.Semiconj fbc gb gc → Function.Semiconj (fbc ∘ fab) ga gc

If fab : α → β semiconjugates ga to gb and fbc : β → γ semiconjugates gb to gc, then fbc ∘ fab semiconjugates ga to gc. See also Function.Semiconj.comp_left for a version with reversed arguments.

Defined in
Mathlib.Logic.Function.Conjugate
Cited by
2 results in Mathlib
Foundations
Depth 5 from the axioms · uses propext
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Function.Semiconj.comp_left · cited by 2Semiconj.comp_leftFunction.Semiconj.iterate_left · cited by 0Semiconj.iterate_leftFunction.Semiconj · cited by 82Function.SemiconjFunction.Semiconj.eq · cited by 12Semiconj.eqSemiconj.transCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.