1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "nat/order.ma".
16 include "datatypes/bool.ma".
18 naxiom decompose1: ¬(lt O O).
19 naxiom decompose2: ∀n. ¬(lt (S n) O).
21 ndefinition ltb: ∀n,m:nat. lt n m ∨ ¬(lt n m).
24 [ napply or_intror; #H; napply (decompose1 H)
25 | #m'; napply or_introl; napply lt_O_Sn ]
26 ##| #n'; #Hn'; #m; ncases m
27 [ napply or_intror; #H; napply (decompose2 … H)
28 | #m'; ncases (Hn' m')
29 [ #H; napply or_introl; napply le_S_S; napply H
30 | #H; napply or_intror; #K; napply H; napply le_S_S_to_le; napply K]##]