X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Fynat%2Fynat_lt.ma;h=26135550e71f510781a6a03f19a09206b996503d;hb=14a8276e6d877c2281a1fda452ed3e4c150f5d39;hp=6cc21d5bcc60bf6018944835931c20bcfae660df;hpb=32bdf7f107be22a121fab8225c5fae4eb6b33633;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma
index 6cc21d5bc..26135550e 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma
@@ -98,8 +98,12 @@ lemma ylt_fwd_succ2: ∀m,n. m < ⫯n → m ≤ n.
 
 (* inversion and forward lemmas on yle **************************************)
 
-lemma lt_fwd_le: ∀m:ynat. ∀n:ynat. m < n → m ≤ n.
-#m #n * -m -n /3 width=1 by yle_pred_sn, yle_inj, yle_Y/
+lemma ylt_fwd_le_succ1: ∀m,n. m < n → ⫯m ≤ n.
+#m #n * -m -n /2 width=1 by yle_inj/
+qed-.
+
+lemma ylt_fwd_le: ∀m:ynat. ∀n:ynat. m < n → m ≤ n.
+#m #n * -m -n /3 width=1 by lt_to_le, yle_inj/
 qed-.
 
 lemma ylt_yle_false: ∀m:ynat. ∀n:ynat. m < n → n ≤ m → ⊥.
@@ -118,6 +122,13 @@ lemma ylt_O: ∀x. ⫯⫰(yinj x) = yinj x → 0 < x.
 #H destruct
 qed.
 
+(* Properties on predecessor ************************************************)
+
+lemma ylt_pred: ∀m,n. m < n → 0 < m → ⫰m < ⫰n.
+#m #n * -m -n
+/4 width=1 by ylt_inv_inj, ylt_inj, monotonic_lt_pred/
+qed.
+
 (* Properties on successor **************************************************)
 
 lemma ylt_O_succ: ∀n. 0 < ⫯n.
@@ -125,7 +136,7 @@ lemma ylt_O_succ: ∀n. 0 < ⫯n.
 qed.
 
 lemma ylt_succ: ∀m,n. m < n → ⫯m < ⫯n.
-#m #n #H elim H -m -n /3 width=1 by ylt_inj, le_S_S/ 
+#m #n #H elim H -m -n /3 width=1 by ylt_inj, le_S_S/
 qed.
 
 (* Properties on order ******************************************************)