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 79b8f1a0bd461312bde38332273455e1d008184e..d7654a0bb43294fcfc57c6a4605e3b46959243e9 100644 (file)
--- 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-.