arithmetics for λδ

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
index 0454acee027d23a65ce36344164c974d7425a339..b5347a806e4ba2f83c52c93ac6721864aab255c0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma
@@ -44,3 +44,14 @@ lemma nle_pred_sn (m) (n): m ≤ ↑n → ↓m ≤ n.
 #m #n @(nat_ind_succ … m) -m //
 /2 width=1 by nle_pred_bi/
 qed-.
+
+(* Inversions with npred ****************************************************)
+
+(*** le_inv_S1 *)
+lemma nle_inv_succ_sn (m) (n):
+      ↑m ≤ n → ∧∧ m ≤ ↓n & n = ↑↓n.
+#m #n * -n
+[ /2 width=3 by nle_refl, conj/
+| #n #Hn /3 width=1 by nle_des_succ_sn, conj/
+]
+qed-.