commit of the "static" component

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsuba_ldrop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_ldrop.ma
index b32e6ba93913fc6902d836e4cc250c9414a86363..43de659bf42f9965ca567ae2ba22737a38e1819f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_ldrop.ma
@@ -19,45 +19,45 @@ include "basic_2/static/lsuba.ma".
 (* Properties concerning basic local environment slicing ********************)
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsuba_ldrop_O1_conf: ∀L1,L2. L1 ⁝⊑ L2 → ∀K1,e. ⇩[0, e] L1 ≡ K1 →
-                           ∃∃K2. K1 ⁝⊑ K2 & ⇩[0, e] L2 ≡ K2.
-#L1 #L2 #H elim H -L1 -L2
+lemma lsuba_ldrop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                           ∃∃K2. G ⊢ K1 ⁝⊑ K2 & ⇩[s, 0, e] L2 ≡ K2.
+#G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
+| #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
   [ destruct
-    elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK1) -L1 /3 width=3/
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #K1 #e #H
+| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K1 #s #e #H
   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
   [ destruct
-    elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK1) -L1 /3 width=3/
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
 ]
 qed-.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsuba_ldrop_O1_trans: ∀L1,L2. L1 ⁝⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
-                            ∃∃K1. K1 ⁝⊑ K2 & ⇩[0, e] L1 ≡ K1.
-#L1 #L2 #H elim H -L1 -L2
+lemma lsuba_ldrop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
+                            ∃∃K1. G ⊢ K1 ⁝⊑ K2 & ⇩[s, 0, e] L1 ≡ K1.
+#G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
+| #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H
   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
   [ destruct
-    elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK2) -L2 /3 width=3/
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #K2 #e #H
+| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K2 #s #e #H
   elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
   [ destruct
-    elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK2) -L2 /3 width=3/
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
 ]
 qed-.