Definition post_cons_right_zig_zag_of_length {C : category} {n : ℕ} {x y z : C} (gs : zig_zag_of_length n x y) (f : z --> y) : zig_zag_of_length (S n) x z. Proof. revert x y z gs f. induction n as [ | n IHn ]. - intros x y z gs f. exact (z ,, inr (f · inv_from_z_iso gs) ,, identity_z_iso z). - intros x y z gs f. induction gs as [ w gs ]. induction gs as [ g gs ]. induction g as [ g | g ]. + exact (w ,, inl g ,, IHn _ _ _ gs f). + exact (w ,, inr g ,, IHn _ _ _ gs f). 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.