`{Univalence} {A} (B : FibSequence A) E (F G : sig (fib_seq_to_type_fam B) -> E) : F o (seq_colim_sum_to_sum_seq_colim B) == G o (seq_colim_sum_to_sum_seq_colim B) -> F == G. Proof. intro h; srapply (seq_colim_sum_ind B _ (fun _ _ _ => h _)); intros n a b. srapply ((transport_compose _ _ _ _)^ @ _); exact (apD h (glue (sig_seq B) n (a;b))). Defined.
Require Import Basics. Require Import Types. Require Import Diagrams.Diagram. Require Import Diagrams.Sequence. Require Import Diagrams.Cocone. Require Import Colimits.Colimit. Require Import Spaces.Nat.Core. Require Import Homotopy.IdentitySystems.