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 "ground/arith/pnat_plus.ma".
16 include "ground/arith/nat_rplus_succ.ma".
18 (* RIGHT ADDITION FOR NON-NEGATIVE INTEGERS *********************************)
20 (* Constructions with pplus *************************************************)
22 lemma nrplus_inj_dx (p) (q):
26 lemma nrplus_pplus_assoc (p,q:pnat) (n:nat):
29 @(nat_ind_succ … n) -n // #n #IH
30 <nrplus_succ_dx <nrplus_succ_dx <pplus_succ_dx //