int_neg_add@{} (x y : Int) : - (x + y) = - x - y. Proof. induction x as [|x IHx|x IHx] in y |- *. - reflexivity. - rewrite int_add_succ_l. rewrite 2 int_neg_succ. rewrite int_add_pred_l. f_ap. - rewrite int_neg_pred. rewrite int_add_succ_l. rewrite int_add_pred_l. rewrite int_neg_pred. 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.