cfg_to_obj completed (modulo daemons)

[helm.git] / matita / matita / contribs / lambda / paths / standard_order.ma

diff --git a/matita/matita/contribs/lambda/paths/standard_order.ma b/matita/matita/contribs/lambda/paths/standard_order.ma
index 9bf484143fdf517dc5a8c30da85d2c0dd78a4bf6..672ba56f1f8df144ac82393e69365bc7cdc3fd0a 100644 (file)
--- a/matita/matita/contribs/lambda/paths/standard_order.ma
+++ b/matita/matita/contribs/lambda/paths/standard_order.ma
@@ -51,7 +51,7 @@ lemma sle_comp: ∀p1,p2. p1 ≤ p2 → ∀o. (o::p1) ≤ (o::p2).
 qed.
 
 lemma sle_skip_sle: ∀p. p ≤ ◊ → dx::p ≤ ◊.
-#p #H @(star_ind_l ??????? H) -p //
+#p #H @(star_ind_l … p H) -p //
 #p #q #Hpq #_ #H @(sle_step_sn … H) -H /2 width=1/
 qed.
 
@@ -73,6 +73,18 @@ lemma sle_dichotomy: ∀p1,p2:path. p1 ≤ p2 ∨ p2 ≤ p1.
 ]
 qed-.
 
+lemma sle_inv_rc: ∀p,q. p ≤ q → ∀p0. rc::p0 = p →
+                  (∃∃q0. p0 ≤ q0 & rc::q0 = q) ∨
+                  ∃q0. sn::q0 = q.
+#p #q #H elim H -q /3 width=3/
+#q #q0 #_ #Hq0 #IHpq #p0 #H destruct
+elim (IHpq p0 ?) -IHpq // *
+[ #p1 #Hp01 #H
+  elim (sprec_inv_rc … Hq0 … H) -q * /3 width=3/ /4 width=3/
+| #p1 #H elim (sprec_inv_sn … Hq0 … H) -q /3 width=2/
+]
+qed-.
+
 lemma sle_inv_sn: ∀p,q. p ≤ q → ∀p0. sn::p0 = p →
                   ∃∃q0. p0 ≤ q0 & sn::q0 = q.
 #p #q #H elim H -q /2 width=3/
@@ -91,9 +103,13 @@ theorem in_whd_sle: ∀p. in_whd p → ∀q. p ≤ q.
 qed.
 
 lemma sle_nil_inv_in_whd: ∀p. p ≤ ◊ → in_whd p.
-#p #H @(star_ind_l ??????? H) -p // /2 width=3 by sprec_fwd_in_whd/
+#p #H @(star_ind_l … p H) -p // /2 width=3 by sprec_fwd_in_whd/
 qed-.
 
 lemma sle_inv_in_whd: ∀p. (∀q. p ≤ q) → in_whd p.
 /2 width=1 by sle_nil_inv_in_whd/
 qed-.
+
+lemma sle_fwd_in_whd: ∀p,q. p ≤ q → in_whd q → in_whd p.
+#p #q #H @(star_ind_l … p H) -p // /3 width=3 by sprec_fwd_in_whd/
+qed-.