fact: Definition predoublecategory_sq_hor_id_comp (C : predoublecategory_ob_mor_sq_data): UU := (∏ (a b : C) (f: a -v-> b), (sqq (hor_identity a) f f (hor_identity b))) × (∏ (a0 a1 b0 b1 c0 c1 : C) (f0: a0 -v-> a1) (f1: b0 -v-> b1) (f2: c0 -v-> c1) (g0: a0 -h-> b0) (h0: b0 -h-> c0) (g1: a1 -h-> b1) (h1: b1 -h-> c1), (sqq g0 f0 f1 g1) → (sqq h0 f1 f2 h1) → (sqq (g0 ·h h0) f0 f2 (g1 ·h h1)) ).
imports: UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Notations UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence