Definition has_bincoprod_ump_1_left_adjoint_equivalence : bincoprod_ump_1 cone₂. Proof. intros c. use make_bincoprod_1cell. - refine (r₃ · _). exact (bincoprod_ump_1cell Hp (l₁ · bincoprod_cocone_inl c) (l₂ · bincoprod_cocone_inr c)). - exact (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ γ₁') (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ (bincoprod_ump_1cell_inl Hp _ _ _)) (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ ε₁) (lunitor_invertible_2cell _))))))). - exact (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ γ₂') (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ (bincoprod_ump_1cell_inr Hp _ _ _)) (comp_of_invertible_2cell (lassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ ε₂) (lunitor_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.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Properties.ContainsAdjEquiv. Require Import UniMath.Bicategories.Colimits.Coproducts.