arithmetics for λδ

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
index 34a16e01f572fd379ba4ed35b8dece84a669e9ba..5ee4b80eb03427110a773454718d101e8751e579 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
@@ -35,3 +35,14 @@ lemma nlt_minus_sn_bi (o) (m) (n): o ≤ m → m < n → m - o < n - o.
 lapply (nle_minus_sn_bi … o Hmn) -Hmn
 <(nminus_succ_sn … Hom) //
 qed.
+
+(* Destructions with nminus *************************************************)
+
+lemma nlt_fwd_minus_dx (o) (m) (n): m < n - o → o < n.
+#o elim o -o
+[ #m #n <nminus_zero_dx
+  /2 width=3 by le_nlt_trans/
+| #o #IH #m #n <nminus_succ_dx_pred_sn #H
+  /3 width=2 by nlt_inv_pred_dx/
+]
+qed-.