proposition: Lemma cone_eq {C I:category} (c:C^op) (D: I⟶C) (p q:cone (C:=C) c D) : pr1 p ~ pr1 q -> p = q.
proof: Proof. intros h. apply subtypePath. { intro r. apply impred_isaprop; intro i; apply impred_isaprop; intro j; apply impred_isaprop; intro e. apply homset_property. } apply funextsec; intro i; apply h. Qed.
imports: UniMath.Foundations.Preamble UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.RepresentableFunctors.Bifunctor UniMath.CategoryTheory.RepresentableFunctors.Precategories UniMath.MoreFoundations.Tactics