proposition: Lemma plus_mod_lt (m:nat): forall k n, m+n < k -> plus_mod_aux k m n = (m+n)%nat.
proof: Proof. induction m. firstorder. intros. simpl. remember (k - S n) as j. destruct j. lia. assert (S (m + n) = (m + (S n))%nat). 2: { rewrite H0. apply IHm. lia. } lia. Defined.
imports: Coq(Arith Relations Lia) AlmostFull.PropBounded(AlmostFull) AlmostFull.PropBounded(AFConstructions)