(b' : B') : hfiber functor_sum (inr b') <~> hfiber g b'. Proof. simple refine (equiv_adjointify _ _ _ _). - intros [[a|b] p]. + elim (inl_ne_inr _ _ p). + exists b. exact (path_sum_inr _ p). - intros [b p]. exists (inr b). exact (ap inr p). - intros [b p]. apply ap. pose (@isequiv_path_sum A' B' (inr (g b)) (inr b')). exact (eissect (@path_sum A' B' (inr (g b)) (inr b')) p). - intros [[a|b] p]; simpl. + elim (inl_ne_inr _ _ p). + apply ap. pose (@isequiv_path_sum A' B' (inr (g b)) (inr b')). exact (eisretr (@path_sum A' B' (inr (g b)) (inr b')) p). Defined.
Require Import HoTT.Basics. Require Import Types.Empty Types.Unit Types.Prod Types.Sigma. Require Import Types.Bool.