Theorem po_category_is_univalent_iff_is_antisymm (PO : po X) : is_univalent (po_category PO) <-> isantisymm PO. Proof. split. - intros isuni a b relab relba. apply (isotoid _ isuni). exists relab. exists relba. apply make_is_inverse_in_precat; apply po_homsets_isaprop. - intro poasymm. intros ? ?. apply (antisymm_po_category_isweq PO poasymm). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence.