int_add_comm@{} (x y : Int) : x + y = y + x. Proof. induction y as [|y IHy|y IHy] in x |- *. - apply int_add_0_r. - rewrite int_add_succ_l. rewrite <- IHy. by rewrite int_add_succ_r. - rewrite int_add_pred_r. rewrite int_add_pred_l. f_ap. Defined.
Require Import Basics.Overture Basics.Nat Basics.Tactics Basics.Decidable Basics.Equivalences Basics.PathGroupoids Types.Paths Types.Universe. Require Import Spaces.Nat.Core.