X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_lt_pred.ma;h=7ebc811f88a988ed8409504f4f4bd7f1be73184e;hp=2b3502259f796845194b82ee7d94f64ecca9112a;hb=ccf5878f2a2ec7f952f140e162391708a740517b;hpb=5e72e41f4f86814e56d4b00959ccc56c71042a4c

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_pred.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_pred.ma
index 2b3502259..7ebc811f8 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_pred.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/arith/nat_pred_succ.ma".
+include "ground/arith/nat_le_pred.ma".
 include "ground/arith/nat_lt.ma".
 
 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS ***********************************)
@@ -29,3 +29,10 @@ lemma nlt_inv_zero_sn (m): 𝟎 < m → m = ↑↓m.
 #m @(nat_ind … m) -m //
 #H elim (nlt_inv_refl … H)
 qed-.
+
+lemma nlt_inv_pred_dx (m) (n): m < ↓n → ↑m < n.
+#m #n #H >(nlt_inv_zero_sn n)
+[ /2 width=1 by nlt_succ_bi/
+| /3 width=3 by le_nlt_trans, nlt_le_trans/
+]
+qed-.