{n m} : n <= m -> (m - n) + n = m. Proof. intros H. induction n as [|n IHn] in m, H |- *. - lhs nrapply nat_add_zero_r. nrapply nat_sub_zero_r. - destruct m. 1: contradiction (not_lt_zero_r n). lhs nrapply nat_add_succ_r. nrapply (ap nat_succ). nrapply IHn. exact (leq_pred' H). Defined.
Require Import Basics.Overture Basics.Tactics Basics.PathGroupoids