path_sigma_pp_pp' {A : Type} (P : A -> Type) {u1 v1 w1 : A} {u2 : P u1} {v2 : P v1} {w2 : P w1} (p1 : u1 = v1) (q1 : p1 # u2 = v2) (p2 : v1 = w1) (q2 : p2 # v2 = w2) : path_sigma' P (p1 @ p2) (transport_pp P p1 p2 u2 @ ap (transport P p2) q1 @ q2) = path_sigma' P p1 q1 @ path_sigma' P p2 q2 := @path_sigma_pp_pp A P (u1;u2) (v1;v2) (w1;w2) p1 q1 p2 q2.
Require Import HoTT.Basics. Require Import Types.Arrow Types.Paths.