preservation of stratified vaildity through ordinary reduction and static typing

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubsv_ldrop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ldrop.ma
index 55e72c775d39abff2356068102b8ba153418bd83..3897a75fac2a16f9b04d19a7f8aba202603bff68 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ldrop.ma
@@ -19,47 +19,47 @@ include "basic_2/dynamic/lsubsv.ma".
 (* Properties concerning basic local environment slicing ********************)
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsubsv_ldrop_O1_conf: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
-                            ∀K1,e. ⇩[0, e] L1 ≡ K1 →
-                            ∃∃K2. h ⊢ K1 ⊩:⊑[g] K2 & ⇩[0, e] L2 ≡ K2.
-#h #g #L1 #L2 #H elim H -L1 -L2
-[ /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
-  elim (ldrop_inv_O1 … H) -H * #He #HLK1
+lemma lsubsv_ldrop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
+                            ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                            ∃∃K2. G ⊢ K1 ¡⫃[h, g] K2 & ⇩[s, 0, e] L2 ≡ K2.
+#h #g #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #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_refl … 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 lsubsv_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #V1 #W1 #W2 #l #HV1 #HVW1 #HW21 #HW2 #_ #IHL12 #K1 #e #H
-  elim (ldrop_inv_O1 … H) -H * #He #HLK1
+| #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #H2l #_ #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_refl … H) in HL12; -H /3 width=4/
-  | 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=4 by lsubsv_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
 ]
-qed.
+qed-.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsubsv_ldrop_O1_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
-                             ∀K2,e. ⇩[0, e] L2 ≡ K2 →
-                             ∃∃K1. h ⊢ K1 ⊩:⊑[g] K2 & ⇩[0, e] L1 ≡ K1.
-#h #g #L1 #L2 #H elim H -L1 -L2
-[ /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
-  elim (ldrop_inv_O1 … H) -H * #He #HLK2
+lemma lsubsv_ldrop_O1_trans: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
+                             ∀K2,s, e. ⇩[s, 0, e] L2 ≡ K2 →
+                             ∃∃K1. G ⊢ K1 ¡⫃[h, g] K2 & ⇩[s, 0, e] L1 ≡ K1.
+#h #g #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #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_refl … 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 lsubsv_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #V1 #W1 #W2 #l #HV1 #HVW1 #HW21 #HW2 #_ #IHL12 #K2 #e #H
-  elim (ldrop_inv_O1 … H) -H * #He #HLK2
+| #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #H2l #_ #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_refl … H) in HL12; -H /3 width=4/
-  | 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=4 by lsubsv_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
 ]
-qed.
+qed-.