uncommited file found :)

[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 e80380217218b13d13dc41a247c8bf503cb4bff8..7bd51c318fb99f02d2e158395fbd6f56ec7c0a9d 100644 (file)
--- a/matita/matita/lib/arithmetics/nat.ma
+++ b/matita/matita/lib/arithmetics/nat.ma
@@ -439,6 +439,10 @@ theorem decidable_lt: ∀n,m. decidable (n < m).
 theorem le_to_or_lt_eq: ∀n,m:nat. n ≤ m → n < m ∨ n = m.
 #n #m #lenm (elim lenm) /3/ qed.
 
+theorem eq_or_gt: ∀n. 0 = n ∨ 0 < n.
+#n elim (le_to_or_lt_eq 0 n ?) // /2 width=1/
+qed-.
+
 theorem increasing_to_le2: ∀f:nat → nat. increasing f → 
   ∀m:nat. f 0 ≤ m → ∃i. f i ≤ m ∧ m < f (S i).
 #f #incr #m #lem (elim lem)
@@ -682,6 +686,10 @@ lapply (minus_le x y) <H -H #H
 elim (not_le_Sn_n x) #H0 elim (H0 ?) //
 qed-.
 
+lemma plus_le_0: ∀x,y. x + y ≤ 0 → x = 0 ∧ y = 0.
+#x #y #H elim (le_inv_plus_l … H) -H #H1 #H2 /3 width=1/
+qed-.
+
 (* Still more equalities ****************************************************)
 
 theorem eq_minus_O: ∀n,m:nat.