ground_2 milestone: multiple relocation with lists of booleans

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / arith.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
index b23fb9de8280f4fe9efd714c1c4462a07956c4dc..5f8451a27216a16883d4e829526fe51d24190931 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
@@ -12,11 +12,17 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/notation/functions/successor_1.ma".
+include "ground_2/notation/functions/predecessor_1.ma".
 include "arithmetics/nat.ma".
 include "ground_2/lib/star.ma".
 
 (* ARITHMETICAL PROPERTIES **************************************************)
 
+interpretation "nat successor" 'Successor m = (S m).
+
+interpretation "nat predecessor" 'Predecessor m = (pred m).
+
 (* Iota equations ***********************************************************)
 
 lemma pred_O: pred 0 = 0.
@@ -133,6 +139,9 @@ lemma lt_zero_false: ∀n. n < 0 → ⊥.
 #n #H elim (lt_to_not_le … H) -H /2 width=1 by/
 qed-.
 
+lemma lt_le_false: ∀x,y. x < y → y ≤ x → ⊥.
+/3 width=4 by lt_refl_false, lt_to_le_to_lt/ qed-.
+
 lemma pred_inv_refl: ∀m. pred m = m → m = 0.
 * // normalize #m #H elim (lt_refl_false m) //
 qed-.