arithmetics for λδ

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

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 2b3502259f796845194b82ee7d94f64ecca9112a..7ebc811f88a988ed8409504f4f4bd7f1be73184e 100644 (file)
--- 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-.