milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / ynat / ynat_lt.ma

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 ab9cf4565cc365d28ff3d8d94b3a8b2359e91c02..5a1bb14dda71e288b35a90a2e77c4ea046657e46 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma
@@ -135,6 +135,11 @@ lemma ylt_O1: ∀x:ynat. ↑↓x = x → 0 < x.
 #H destruct
 qed.
 
+lemma yle_inv_succ_sn_lt (x:ynat) (y:ynat):
+      ↑x ≤ y → ∧∧ x ≤ ↓y & 0 < y.
+#x #y #H elim (yle_inv_succ1 … H) -H /3 width=2 by ylt_O1, conj/
+qed-.
+
 (* Properties on predecessor ************************************************)
 
 lemma ylt_pred: ∀m,n:ynat. m < n → 0 < m → ↓m < ↓n.
@@ -144,7 +149,7 @@ qed.
 
 (* Properties on successor **************************************************)
 
-lemma ylt_O_succ: ∀n. 0 < ↑n.
+lemma ylt_O_succ: ∀x:ynat. 0 < ↑x.
 * /2 width=1 by ylt_inj/
 qed.
 
@@ -199,7 +204,7 @@ lemma yle_ylt_trans: ∀x:ynat. ∀y:ynat. ∀z:ynat. y < z → x ≤ y → x <
 ]
 qed-.
 
-lemma le_ylt_trans (x) (y) (z): x ≤ y → yinj y < z → yinj x < z.  
+lemma le_ylt_trans (x) (y) (z): x ≤ y → yinj y < z → yinj x < z.
 /3 width=3 by yle_ylt_trans, yle_inj/
 qed-.
 
@@ -223,7 +228,7 @@ theorem ylt_trans: Transitive … ylt.
 ]
 qed-.
 
-lemma lt_ylt_trans (x) (y) (z): x < y → yinj y < z → yinj x < z.  
+lemma lt_ylt_trans (x) (y) (z): x < y → yinj y < z → yinj x < z.
 /3 width=3 by ylt_trans, ylt_inj/
 qed-.