(x y : Int) : x + y.-1 = (x + y).-1. Proof. induction x as [|x IHx|[] IHx] in y |- *. - reflexivity. - rewrite 2 int_add_succ_l. rewrite IHx. by rewrite int_pred_succ, int_succ_pred. - reflexivity. - rewrite 2 int_add_pred_l. by rewrite IHx. Defined.
Require Import Basics.Overture Basics.Nat Basics.Tactics Basics.Decidable Basics.Equivalences Basics.PathGroupoids Types.Paths Types.Universe. Require Import Spaces.Nat.Core.