{A B} {z z' : A + B} : path_sum o (@path_sum_inv _ _ z z') == idmap := fun p => match p as p in (_ = z') return path_sum (path_sum_inv p) = p with | 1 => match z as z return (@path_sum _ _ z z) (path_sum_inv 1) = 1 with | inl _ => 1 | inr _ => 1 end end.
Require Import HoTT.Basics. Require Import Types.Empty Types.Unit Types.Prod Types.Sigma. Require Import Types.Bool.