propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / nat_rplus.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground/arith/nat_iter.ma".
+
+(* RIGHT ADDITION FOR NON-NEGATIVE INTEGERS *********************************)
+
+definition nrplus: pnat → nat → pnat ≝
+           λp,n. psucc^n p.
+
+interpretation
+  "right plus (non-negative integers)"
+  'plus p n = (nrplus p n).
+
+(* Basic constructions ******************************************************)
+
+lemma nrplus_zero_dx (p): p = p + 𝟎.
+// qed.
+
+lemma nrplus_unit_dx (p): ↑p = p + 𝟏.
+// qed.
+
+lemma nrplus_succ_sn (p) (n): ↑(p+n) = ↑p + n.
+#p #n @(niter_appl … psucc)
+qed.