{A B : Type} {x000 x010 x100 x110 x001 x011 x101 x111 : A} {p0i0 : x000 = x010} {p1i0 : x100 = x110} {pi00 : x000 = x100} {pi10 : x010 = x110} {p0i1 : x001 = x011} {p1i1 : x101 = x111} {pi01 : x001 = x101} {pi11 : x011 = x111} {p00i : x000 = x001} {p01i : x010 = x011} {p10i : x100 = x101} {p11i : x110 = x111} {s0ii : PathSquare p0i0 p0i1 p00i p01i} {s1ii : PathSquare p1i0 p1i1 p10i p11i} {sii0 : PathSquare p0i0 p1i0 pi00 pi10} {sii1 : PathSquare p0i1 p1i1 pi01 pi11} {si0i : PathSquare p00i p10i pi00 pi01} {si1i : PathSquare p01i p11i pi10 pi11} {cube : PathCube s0ii s1ii sii0 sii1 si0i si1i} {b000 b010 b100 b110 b001 b011 b101 b111 : B} {bp0i0 : b000 = b010} {bp1i0 : b100 = b110} {bpi00 : b000 = b100} {bpi10 : b010 = b110} {bp0i1 : b001 = b011} {bp1i1 : b101 = b111} {bpi01 : b001 = b101} {bpi11 : b011 = b111} {bp00i : b000 = b001} {bp01i : b010 = b011} {bp10i : b100 = b101} {bp11i : b110 = b111} {bs0ii : PathSquare bp0i0 bp0i1 bp00i bp01i} {bs1ii : PathSquare bp1i0 bp1i1 bp10i bp11i} {bsii0 : PathSquare bp0i0 bp1i0 bpi00 bpi10} {bsii1 : PathSquare bp0i1 bp1i1 bpi01 bpi11} {bsi0i : PathSquare bp00i bp10i bpi00 bpi01} {bsi1i : PathSquare bp01i bp11i bpi10 bpi11} : PathCube bs0ii bs1ii bsii0 bsii1 bsi0i bsi1i <~> DPathCube (fun _ => B) cube (ds_const bs0ii) (ds_const bs1ii) (ds_const bsii0) (ds_const bsii1) (ds_const bsi0i) (ds_const bsi1i). Proof. by destruct cube. Defined.
Require Import Basics. Require Import Cubical.DPath. Require Import Cubical.PathSquare. Require Import Cubical.DPathSquare. Require Import Cubical.PathCube.