Definition precomp_z_iso_zig_zag_of_length {C : category} {n : ℕ} {x y z : C} (fs : zig_zag_of_length n y z) (i : z_iso x y) : zig_zag_of_length n x z. Proof. revert x y z fs i. induction n as [ | n IHn ]. - intros x y z fs i. exact (z_iso_comp i fs). - intros x y z fs i. induction fs as [ w fs ]. induction fs as [ f fs ]. induction f as [ f | f ]. + exact (w ,, inl (i · f) ,, fs). + exact (w ,, inr (f · inv_from_z_iso i) ,, fs). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Groupoids.