proposition: Lemma faithful_reflects_commutative_triangle {C D : precategory} (F : functor C D) (FF : faithful F) {a b c : ob C} (f : C ⟦a, b⟧) (g : C ⟦b, c⟧) (h : C ⟦a, c⟧) : # F f · # F g = # F h → f · g = h.
proof: Proof. intros feq. apply (Injectivity (# F)). - apply isweqonpathsincl, FF. - exact (functor_comp F f g @ feq). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Univalence UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence