proposition: Proposition prod_from_underlying_arr_map_eq₂ (f : I_{V} --> BPV (E ⦃ w, x ⦄) (E ⦃ w, y ⦄)) : prod_from_underlying_arr_map f · binary_prod_enriched_to_prod BPV a w = f.
proof: Proof. unfold prod_from_underlying_arr_map. use (BinProductArrowsEq _ _ _ (BPV (E ⦃ w, x ⦄) (E ⦃ w, y ⦄))). - unfold binary_prod_enriched_to_prod. rewrite !assoc'. rewrite !BinProductPr1Commutes. rewrite enriched_from_arr_postcomp. refine (_ @ enriched_from_to_arr E _). apply maponpaths. apply (BinProductPr1Commutes _ _ _ (make_BinProduct C x y a _ _ prod)). - unfold binary_prod_enriched_to_prod. rewrite !assoc'. rewrite !BinProductPr2Commutes. rewrite enriched_from_arr_postcomp. refine (_ @ enriched_from_to_arr E _). apply maponpaths. apply (BinProductPr2Commutes _ _ _ (make_BinProduct C x y a _ _ prod)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.Limits.BinProducts