{A B C D E F} (f : A -> C) (g : B -> D) (h : C -> E) (i : D -> F) : functor_join (h o f) (i o g) == functor_join h i o functor_join f g. Proof. snrapply Join_ind_FlFr. 1,2: reflexivity. intros a b. simpl. apply equiv_p1_1q. lhs nrapply functor_join_beta_jglue; symmetry. lhs nrapply (ap_compose (functor_join f g) _ (jglue a b)). lhs nrefine (ap _ (functor_join_beta_jglue _ _ _ _)). apply functor_join_beta_jglue. Defined.
Require Import Basics Types. Require Import Cubical.DPath Cubical.PathSquare. Require Import NullHomotopy. Require Import Extensions. Require Import Colimits.Pushout. Require Import Truncations.Core Truncations.Connectedness. Require Import Pointed.Core. Require Import WildCat. Require Import Spaces.Nat.Core.