proposition: Theorem lt_ind : forall (A : positive -> Prop) (n : positive), A (succ n) -> (forall m : positive, n < m -> A m -> A (succ m)) -> forall m : positive, n < m -> A m.
proof: Proof. intros A n AB AS m. induction m using peano_ind; intros H. - elim (nlt_1_r _ H). - apply lt_succ_r, le_lteq in H. destruct H as [H|H]; subst; auto. Qed.
imports: BinNums Eqdep_dec EqdepFacts RelationClasses Morphisms Setoid Equalities Orders OrdersFacts GenericMinMax PeanoNat BinPosDef