proposition: Proposition enriched_rezk_completion_ump_full_isaprop : isaprop (∑ (f : G₁ x --> G₂ x), ∏ (w : C₁) (i : z_iso (F w) x), τ w · #G₂ i = #G₁ i · f).
proof: Proof. use invproofirrelevance. intros φ₁ φ₂. use subtypePath. { intro. repeat (use impred ; intro). apply homset_property. } assert (H := HF₁ x). revert H. use factor_through_squash. { apply homset_property. } intros w. induction w as [ w i ]. use (cancel_z_iso' (functor_on_z_iso G₁ i)). exact (!(pr2 φ₁ w i) @ pr2 φ₂ w i). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation UniMath.CategoryTheory.EnrichedCats.FullyFaithful UniMath.CategoryTheory.EnrichedCats.Examples.FunctorCategory UniMath.CategoryTheory.EnrichedCats.Examples.Precomposition UniMath.CategoryTheory.Monoidal.Categories