proposition: Lemma minus_ge : forall a b, a <= b -> cut_minus a b =N= 0.
proof: Proof. unfold cut_minus,nat_cut_minus. intros a b;revert a;induction b as [|b IH];intros [|a];simpl. - split. - intros E;destruct (not_lt_0 _ E). - split. - intros E. apply IH;apply le_S_S,E. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.naturals HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.semirings HoTT.Classes.theory.apartness