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[helm.git] / matita / matita / lib / arithmetics / nat.ma

diff --git a/matita/matita/lib/arithmetics/nat.ma b/matita/matita/lib/arithmetics/nat.ma
index d806697b8257d3c3922d478404593c0bfca1f80f..81d6c9310247dc42c5f2d0d76e66a986ae1d45fc 100644 (file)
--- a/matita/matita/lib/arithmetics/nat.ma
+++ b/matita/matita/lib/arithmetics/nat.ma
@@ -450,8 +450,16 @@ lemma lt_or_ge: ∀m,n. m < n ∨ n ≤ m.
 #m #n elim (decidable_lt m n) /2 width=1/ /3 width=1/
 qed-.
 
+lemma le_or_ge: ∀m,n. m ≤ n ∨ n ≤ m.
+#m #n elim (decidable_le m n) /2 width=1/ /4 width=2/
+qed-.
+
 (* More general conclusion **************************************************)
 
+theorem nat_ind_plus: ∀R:predicate nat.
+                      R 0 → (∀n. R n → R (n + 1)) → ∀n. R n.
+/3 width=1 by nat_ind/ qed-.
+
 theorem lt_O_n_elim: ∀n:nat. 0 < n → 
   ∀P:nat → Prop.(∀m:nat.P (S m)) → P n.
 #n (elim n) // #abs @False_ind /2/ @absurd