proposition: Lemma z_iso_disp_prod_weq (x : C) (xx1 xx1' : D1 x) (xx2 xx2' : D2 x) : @z_iso_disp _ dirprod_disp_cat _ _ (identity_z_iso x) (xx1,, xx2) (xx1',, xx2') ≃ (z_iso_disp (identity_z_iso x) xx1 xx1') × (z_iso_disp (identity_z_iso x) xx2 xx2').
proof: Proof. exists (z_iso_disp_prod1 xx1 xx1' xx2 xx2'). use isweq_iso. - apply z_iso_disp_prod2. - apply z_iso_disp_prod21. - apply z_iso_disp_prod12. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing