Mathlib Map

Theorems · Definition · order theory

RelHom.comp

{α : Type u_1} →
  {β : Type u_2} →
    {γ : Type u_3} → {r : α → α → Prop} → {s : β → β → Prop} → {t : γ → γ → Prop} → s →r t → r →r s → r →r t

Composition of two relation homomorphisms is a relation homomorphism.

Defined in
Mathlib.Order.RelIso.Basic
Cited by
7 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.Hom.comp · cited by 20Hom.compRelHom.comp_apply · cited by 6RelHom.comp_applyRelIso.relHomCongr · cited by 4RelIso.relHomCongrRelHom.comp_assoc · cited by 0RelHom.comp_assocRelHom.comp_id · cited by 0RelHom.comp_idRelHom.id_comp · cited by 0RelHom.id_compRelIso.relHomCongr_apply · cited by 0RelIso.relHomCongr_applyRelHom.mul_def · cited by 0RelHom.mul_defRelIso.relHomCongr_symm_apply · cited by 0RelIso.relHomCongr_symm_a…DFunLike.coe · cited by 62936DFunLike.coeRelHom · cited by 49RelHomRelHom.compCITED BYCITES

Cites2

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

Cited by9

Results whose statement or proof uses this declaration.