Definition has_binprod_ump_1_left_adjoint_equivalence : binprod_ump_1 cone₂. Proof. intros c. use make_binprod_1cell. - refine (_ · l₃). exact (binprod_ump_1cell Hp (binprod_cone_pr1 c · r₁) (binprod_cone_pr2 c · r₂)). - exact (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ γ₁) (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ (binprod_ump_1cell_pr1 Hp _ (binprod_cone_pr1 c · r₁) (binprod_cone_pr2 c · r₂))) (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ ε₁) (runitor_invertible_2cell _))))))). - exact (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ γ₂) (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ (binprod_ump_1cell_pr2 Hp _ (binprod_cone_pr1 c · r₁) (binprod_cone_pr2 c · r₂))) (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ ε₂) (runitor_invertible_2cell _))))))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Properties.ContainsAdjEquiv. Require Import UniMath.Bicategories.Limits.Products.