proposition: Lemma ineq_sub' (n k : nat) : k < n -> n - k = (n - k.+1).+1.
proof: Proof. intro ineq. destruct n. - contradiction (not_lt_n_0 k). - change (n.+1 - k.+1) with (n - k). apply leq_S_n in ineq. apply (nataddsub_assoc_lemma _). Defined.
imports: Basics Spaces.Nat.Core