commit of the "relocation" component with the new definition of ldrop,

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lsubr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lsubr.ma
index faf254e36e6aabeb10892a6e0b4b2a90ff4b7bca..e96683a80e96fc536957699695a2065bc013b7e4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lsubr.ma
@@ -30,7 +30,7 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma lsubr_refl: ∀L. L ⊑ L.
-#L elim L -L // /2 width=1/
+#L elim L -L /2 width=1 by lsubr_sort, lsubr_bind/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -48,8 +48,8 @@ lemma lsubr_inv_atom1: ∀L2. ⋆ ⊑ L2 → L2 = ⋆.
 fact lsubr_inv_abst1_aux: ∀L1,L2. L1 ⊑ L2 → ∀K1,W. L1 = K1.ⓛW →
                           L2 = ⋆ ∨ ∃∃K2. K1 ⊑ K2 & L2 = K2.ⓛW.
 #L1 #L2 * -L1 -L2
-[ #L #K1 #W #H destruct /2 width=1/
-| #I #L1 #L2 #V #HL12 #K1 #W #H destruct /3 width=3/
+[ #L #K1 #W #H destruct /2 width=1 by or_introl/
+| #I #L1 #L2 #V #HL12 #K1 #W #H destruct /3 width=3 by ex2_intro, or_intror/
 | #L1 #L2 #V1 #V2 #_ #K1 #W #H destruct
 ]
 qed-.
@@ -62,7 +62,7 @@ fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⊑ L2 → ∀K2,W. L2 = K2.ⓓW →
                           ∃∃K1. K1 ⊑ K2 & L1 = K1.ⓓW.
 #L1 #L2 * -L1 -L2
 [ #L #K2 #W #H destruct
-| #I #L1 #L2 #V #HL12 #K2 #W #H destruct /2 width=3/
+| #I #L1 #L2 #V #HL12 #K2 #W #H destruct /2 width=3 by ex2_intro/
 | #L1 #L2 #V1 #V2 #_ #K2 #W #H destruct
 ]
 qed-.
@@ -74,32 +74,34 @@ lemma lsubr_inv_abbr2: ∀L1,K2,W. L1 ⊑ K2.ⓓW →
 (* Basic forward lemmas *****************************************************)
 
 lemma lsubr_fwd_length: ∀L1,L2. L1 ⊑ L2 → |L2| ≤ |L1|.
-#L1 #L2 #H elim H -L1 -L2 // /2 width=1/
+#L1 #L2 #H elim H -L1 -L2 /2 width=1 by monotonic_le_plus_l/
 qed-.
 
 lemma lsubr_fwd_ldrop2_bind: ∀L1,L2. L1 ⊑ L2 →
-                             ∀I,K2,W,i. ⇩[0, i] L2 ≡ K2.ⓑ{I}W →
-                             (∃∃K1. K1 ⊑ K2 & ⇩[0, i] L1 ≡ K1.ⓑ{I}W) ∨
-                             ∃∃K1,V. K1 ⊑ K2 & ⇩[0, i] L1 ≡ K1.ⓓⓝW.V & I = Abst.
+                             ∀I,K2,W,s,i. ⇩[s, 0, i] L2 ≡ K2.ⓑ{I}W →
+                             (∃∃K1. K1 ⊑ K2 & ⇩[s, 0, i] L1 ≡ K1.ⓑ{I}W) ∨
+                             ∃∃K1,V. K1 ⊑ K2 & ⇩[s, 0, i] L1 ≡ K1.ⓓⓝW.V & I = Abst.
 #L1 #L2 #H elim H -L1 -L2
-[ #L #I #K2 #W #i #H
+[ #L #I #K2 #W #s #i #H
   elim (ldrop_inv_atom1 … H) -H #H destruct
-| #J #L1 #L2 #V #HL12 #IHL12 #I #K2 #W #i #H
+| #J #L1 #L2 #V #HL12 #IHL12 #I #K2 #W #s #i #H
   elim (ldrop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /3 width=3/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 * /4 width=3/ /4 width=4/
+  [ /3 width=3 by ldrop_pair, ex2_intro, or_introl/
+  | elim (IHL12 … HLK2) -IHL12 -HLK2 *
+    /4 width=4 by ldrop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
   ]
-| #L1 #L2 #V1 #V2 #HL12 #IHL12 #I #K2 #W #i #H
+| #L1 #L2 #V1 #V2 #HL12 #IHL12 #I #K2 #W #s #i #H
   elim (ldrop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /3 width=4/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 * /4 width=3/ /4 width=4/
+  [ /3 width=4 by ldrop_pair, ex3_2_intro, or_intror/
+  | elim (IHL12 … HLK2) -IHL12 -HLK2 *
+    /4 width=4 by ldrop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
   ]
 ]
 qed-.
 
 lemma lsubr_fwd_ldrop2_abbr: ∀L1,L2. L1 ⊑ L2 →
-                             ∀K2,V,i. ⇩[0, i] L2 ≡ K2.ⓓV →
-                             ∃∃K1. K1 ⊑ K2 & ⇩[0, i] L1 ≡ K1.ⓓV.
-#L1 #L2 #HL12 #K2 #V #i #HLK2 elim (lsubr_fwd_ldrop2_bind … HL12 … HLK2) -L2 // *
+                             ∀K2,V,s,i. ⇩[s, 0, i] L2 ≡ K2.ⓓV →
+                             ∃∃K1. K1 ⊑ K2 & ⇩[s, 0, i] L1 ≡ K1.ⓓV.
+#L1 #L2 #HL12 #K2 #V #s #i #HLK2 elim (lsubr_fwd_ldrop2_bind … HL12 … HLK2) -L2 // *
 #K1 #W #_ #_ #H destruct
 qed-.