notational change of lift, drop, and gget

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
index 0595e7c208346bd0eb0cc6c75edd0146bf7d6d93..111da17511225ed78d90f289af41e88278639910 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
@@ -13,14 +13,14 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqc_2.ma".
-include "basic_2/relocation/ldrop.ma".
+include "basic_2/substitution/drop.ma".
 
 (* RESTRICTED LOCAL ENVIRONMENT REFINEMENT **********************************)
 
 inductive lsubr: relation lenv ≝
-| lsubr_sort: ∀L. lsubr L (⋆)
-| lsubr_bind: ∀I,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubr_abst: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
+| lsubr_atom: ∀L. lsubr L (⋆)
+| lsubr_pair: ∀I,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I}V) (L2.ⓑ{I}V)
+| lsubr_beta: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
 interpretation
@@ -30,7 +30,7 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma lsubr_refl: ∀L. L ⫃ L.
-#L elim L -L /2 width=1 by lsubr_sort, lsubr_bind/
+#L elim L -L /2 width=1 by lsubr_atom, lsubr_pair/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -77,31 +77,31 @@ lemma lsubr_fwd_length: ∀L1,L2. L1 ⫃ L2 → |L2| ≤ |L1|.
 #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,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.
+lemma lsubr_fwd_drop2_pair: ∀L1,L2. L1 ⫃ L2 →
+                            ∀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 #s #i #H
-  elim (ldrop_inv_atom1 … H) -H #H destruct
+  elim (drop_inv_atom1 … H) -H #H destruct
 | #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 by ldrop_pair, ex2_intro, or_introl/
+  elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
+  [ /3 width=3 by drop_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/
+    /4 width=4 by drop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
   ]
 | #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 by ldrop_pair, ex3_2_intro, or_intror/
+  elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
+  [ /3 width=4 by drop_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/
+    /4 width=4 by drop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
   ]
 ]
 qed-.
 
-lemma lsubr_fwd_ldrop2_abbr: ∀L1,L2. L1 ⫃ 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 // *
+lemma lsubr_fwd_drop2_abbr: ∀L1,L2. L1 ⫃ 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_drop2_pair … HL12 … HLK2) -L2 // *
 #K1 #W #_ #_ #H destruct
 qed-.