X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_lt_minus.ma;h=d7654a0bb43294fcfc57c6a4605e3b46959243e9;hp=79b8f1a0bd461312bde38332273455e1d008184e;hb=19b0a814861157ba05f23877d5cd94059f52c2e8;hpb=21de0d35017656c5a55528390b54b0b2ae395b44

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 79b8f1a0b..d7654a0bb 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_minus.ma
@@ -26,13 +26,22 @@ lapply (nle_minus_sn_bi … o Hmn) -Hmn
 <(nminus_succ_sn … Hom) //
 qed.
 
+(*** monotonic_lt_minus_r *)
+lemma nlt_minus_dx_bi (o) (m) (n):
+      m < o -> m < n → o-n < o-m.
+#o #m #n #Ho #H
+lapply (nle_minus_dx_bi … o H) -H #H
+@(le_nlt_trans … H) -n
+@nlt_i >(nminus_succ_sn … Ho) //
+qed.
+
 (* Destructions with nminus *************************************************)
 
 (*** minus_pred_pred *)
 lemma nminus_pred_bi (m) (n): 𝟎 < m → 𝟎 < n → n - m = ↓n - ↓m.
 #m #n #Hm #Hn
->(nlt_inv_zero_sn … Hm) in ⊢ (??%?); -Hm
->(nlt_inv_zero_sn … Hn) in ⊢ (??%?); -Hn
+>(nlt_des_gen … Hm) in ⊢ (??%?); -Hm
+>(nlt_des_gen … Hn) in ⊢ (??%?); -Hn
 //
 qed-.