X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_lt_pred.ma;h=c319006fc4df70d9fadeffe0e3ed266d1b823f8d;hb=21de0d35017656c5a55528390b54b0b2ae395b44;hp=16e5bb239708419fbef4c0d6b9574325052a221f;hpb=74c6905907b0bca229366d52450e2a6982b5b8be;p=helm.git

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 16e5bb239..c319006fc 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_pred.ma
@@ -12,20 +12,27 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/arith/nat_pred_succ.ma".
+include "ground/arith/nat_le_pred.ma".
 include "ground/arith/nat_lt.ma".
 
-(* NON-NEGATIVE INTEGERS ****************************************************)
+(* STRICT ORDER FOR NON-NEGATIVE INTEGERS ***********************************)
 
-(* Basic constructions with pred ********************************************)
+(* Constructions with npred *************************************************)
 
 lemma nlt_zero_sn (m): m = ↑↓m → 𝟎 < m.
 // qed.
 
-(* Basic inversions with pred ***********************************************)
+(* Inversions with npred ****************************************************)
 
 (*** S_pred *)
 lemma nlt_inv_zero_sn (m): 𝟎 < m → m = ↑↓m.
-#m @(nat_ind … m) -m //
+#m @(nat_ind_succ … 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-.