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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground/arith/pnat_plus.ma".
16 include "ground/arith/nat_pred.ma".
17 include "ground/arith/nat_rplus_succ.ma".
19 (* RIGHT ADDITION FOR NON-NEGATIVE INTEGERS *********************************)
21 (* Constructions with pplus *************************************************)
23 lemma nrplus_inj_dx (p) (q):
27 lemma nrplus_pnpred_dx (p) (q):
28 pnpred (p+q) = nrplus p (pnpred q).
32 lemma nrplus_pplus_assoc (p,q:pnat) (n:nat):
35 @(nat_ind_succ … n) -n // #n #IH
36 <nrplus_succ_dx <nrplus_succ_dx <pplus_succ_dx //