int_mul_pred_l@{} (x y : Int) : x.-1 * y = -y + x * y. Proof. induction x as [|x IHx|[] IHx] in y |- *. - reflexivity. - rewrite int_mul_succ_l. rewrite int_succ_pred. rewrite int_add_assoc. by rewrite int_add_neg_l. - reflexivity. - reflexivity. Defined.
Require Import Basics.Overture Basics.Nat Basics.Tactics Basics.Decidable Basics.Equivalences Basics.PathGroupoids Types.Paths Types.Universe. Require Import Spaces.Nat.Core.