X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Flib%2Farith.ma;h=d181e88cf3f385f1e8ae993f172461810ca31036;hb=750305d95b8f6bb40b5be0e9dfd05d42b256f2a1;hp=5f8451a27216a16883d4e829526fe51d24190931;hpb=ea6b4322051d3eb1794bfca3928f6e1773f971ba;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
index 5f8451a27..d181e88cf 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/lib/arith.ma
@@ -106,6 +106,9 @@ lemma monotonic_lt_pred: ∀m,n. m < n → O < m → pred m < pred n.
 @le_S_S_to_le >S_pred /2 width=3 by transitive_lt/
 qed.
 
+lemma lt_S_S: ∀x,y. x < y → ⫯x < ⫯y.
+/2 width=1 by le_S_S/ qed.
+
 lemma arith_j: ∀x,y,z. x-y-1 ≤ x-(y-z)-1.
 /3 width=1 by monotonic_le_minus_l, monotonic_le_minus_r/ qed.
 
@@ -174,6 +177,19 @@ lemma zero_eq_plus: ∀x,y. 0 = x + y → 0 = x ∧ 0 = y.
 * /2 width=1 by conj/ #x #y normalize #H destruct
 qed-.
 
+lemma lt_S_S_to_lt: ∀x,y. ⫯x < ⫯y → x < y.
+/2 width=1 by le_S_S_to_le/ qed-.
+
+lemma lt_elim: ∀R:relation nat.
+               (∀n2. R O (⫯n2)) →
+               (∀n1,n2. R n1 n2 → R (⫯n1) (⫯n2)) →
+               ∀n2,n1. n1 < n2 → R n1 n2.
+#R #IH1 #IH2 #n2 elim n2 -n2
+[ #n1 #H elim (lt_le_false … H) -H //
+| #n2 #IH * /4 width=1 by lt_S_S_to_lt/
+]
+qed-.
+
 (* Iterators ****************************************************************)
 
 (* Note: see also: lib/arithemetics/bigops.ma *)