notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/drops.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/drops.ma
index 4508cf6a38c168ac8d41e156220289f22f5e1afa..3a25465640956469ca7d7c65ad2d9c8ffcf0d895 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/drops.ma
@@ -16,14 +16,14 @@ include "basic_2/notation/relations/rdropstar_3.ma".
 include "basic_2/notation/relations/rdropstar_4.ma".
 include "basic_2/substitution/drop.ma".
 include "basic_2/multiple/mr2_minus.ma".
-include "basic_2/multiple/lifts.ma".
+include "basic_2/multiple/lifts_vector.ma".
 
 (* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
 
 inductive drops (s:bool): list2 nat nat → relation lenv ≝
 | drops_nil : ∀L. drops s (◊) L L
 | drops_cons: ∀L1,L,L2,des,d,e.
-              drops s des L1 L â\86\92 â\87©[s, d, e] L ≡ L2 → drops s ({d, e} @ des) L1 L2
+              drops s des L1 L â\86\92 â¬\87[s, d, e] L ≡ L2 → drops s ({d, e} @ des) L1 L2
 .
 
 interpretation "iterated slicing (local environment) abstract"
@@ -33,20 +33,33 @@ interpretation "iterated slicing (local environment) general"
    'RDropStar des T1 T2 = (drops true des T1 T2).
 *)
 
+definition l_liftable1: relation2 lenv term → predicate bool ≝
+                        λR,s. ∀K,T. R K T → ∀L,d,e. ⬇[s, d, e] L ≡ K →
+                        ∀U. ⬆[d, e] T ≡ U → R L U.
+
+definition l_liftables1: relation2 lenv term → predicate bool ≝
+                         λR,s. ∀L,K,des. ⬇*[s, des] L ≡ K →
+                         ∀T,U. ⬆*[des] T ≡ U → R K T → R L U.
+
+definition l_liftables1_all: relation2 lenv term → predicate bool ≝
+                             λR,s. ∀L,K,des. ⬇*[s, des] L ≡ K →
+                             ∀Ts,Us. ⬆*[des] Ts ≡ Us → 
+                             all … (R K) Ts → all … (R L) Us.
+
 (* Basic inversion lemmas ***************************************************)
 
-fact drops_inv_nil_aux: â\88\80L1,L2,s,des. â\87©*[s, des] L1 ≡ L2 → des = ◊ → L1 = L2.
+fact drops_inv_nil_aux: â\88\80L1,L2,s,des. â¬\87*[s, des] L1 ≡ L2 → des = ◊ → L1 = L2.
 #L1 #L2 #s #des * -L1 -L2 -des //
 #L1 #L #L2 #d #e #des #_ #_ #H destruct
 qed-.
 
 (* Basic_1: was: drop1_gen_pnil *)
-lemma drops_inv_nil: â\88\80L1,L2,s. â\87©*[s, ◊] L1 ≡ L2 → L1 = L2.
+lemma drops_inv_nil: â\88\80L1,L2,s. â¬\87*[s, ◊] L1 ≡ L2 → L1 = L2.
 /2 width=4 by drops_inv_nil_aux/ qed-.
 
-fact drops_inv_cons_aux: â\88\80L1,L2,s,des. â\87©*[s, des] L1 ≡ L2 →
+fact drops_inv_cons_aux: â\88\80L1,L2,s,des. â¬\87*[s, des] L1 ≡ L2 →
                          ∀d,e,tl. des = {d, e} @ tl →
-                         â\88\83â\88\83L. â\87©*[s, tl] L1 â\89¡ L & â\87©[s, d, e] L ≡ L2.
+                         â\88\83â\88\83L. â¬\87*[s, tl] L1 â\89¡ L & â¬\87[s, d, e] L ≡ L2.
 #L1 #L2 #s #des * -L1 -L2 -des
 [ #L #d #e #tl #H destruct
 | #L1 #L #L2 #des #d #e #HT1 #HT2 #hd #he #tl #H destruct
@@ -55,15 +68,15 @@ fact drops_inv_cons_aux: ∀L1,L2,s,des. ⇩*[s, des] L1 ≡ L2 →
 qed-.
 
 (* Basic_1: was: drop1_gen_pcons *)
-lemma drops_inv_cons: â\88\80L1,L2,s,d,e,des. â\87©*[s, {d, e} @ des] L1 ≡ L2 →
-                      â\88\83â\88\83L. â\87©*[s, des] L1 â\89¡ L & â\87©[s, d, e] L ≡ L2.
+lemma drops_inv_cons: â\88\80L1,L2,s,d,e,des. â¬\87*[s, {d, e} @ des] L1 ≡ L2 →
+                      â\88\83â\88\83L. â¬\87*[s, des] L1 â\89¡ L & â¬\87[s, d, e] L ≡ L2.
 /2 width=3 by drops_inv_cons_aux/ qed-.
 
 lemma drops_inv_skip2: ∀I,s,des,des2,i. des ▭ i ≡ des2 →
-                       â\88\80L1,K2,V2. â\87©*[s, des2] L1 ≡ K2. ⓑ{I} V2 →
+                       â\88\80L1,K2,V2. â¬\87*[s, des2] L1 ≡ K2. ⓑ{I} V2 →
                        ∃∃K1,V1,des1. des + 1 ▭ i + 1 ≡ des1 + 1 &
-                                     â\87©*[s, des1] K1 ≡ K2 &
-                                     â\87§*[des1] V2 ≡ V1 &
+                                     â¬\87*[s, des1] K1 ≡ K2 &
+                                     â¬\86*[des1] V2 ≡ V1 &
                                      L1 = K1. ⓑ{I} V1.
 #I #s #des #des2 #i #H elim H -des -des2 -i
 [ #i #L1 #K2 #V2 #H
@@ -83,8 +96,8 @@ qed-.
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: drop1_skip_bind *)
-lemma drops_skip: â\88\80L1,L2,s,des. â\87©*[s, des] L1 â\89¡ L2 â\86\92 â\88\80V1,V2. â\87§*[des] V2 ≡ V1 →
-                  â\88\80I. â\87©*[s, des + 1] L1.ⓑ{I}V1 ≡ L2.ⓑ{I}V2.
+lemma drops_skip: â\88\80L1,L2,s,des. â¬\87*[s, des] L1 â\89¡ L2 â\86\92 â\88\80V1,V2. â¬\86*[des] V2 ≡ V1 →
+                  â\88\80I. â¬\87*[s, des + 1] L1.ⓑ{I}V1 ≡ L2.ⓑ{I}V2.
 #L1 #L2 #s #des #H elim H -L1 -L2 -des
 [ #L #V1 #V2 #HV12 #I
   >(lifts_inv_nil … HV12) -HV12 //
@@ -93,4 +106,17 @@ lemma drops_skip: ∀L1,L2,s,des. ⇩*[s, des] L1 ≡ L2 → ∀V1,V2. ⇧*[des]
 ].
 qed.
 
+lemma l1_liftable_liftables: ∀R,s. l_liftable1 R s → l_liftables1 R s.
+#R #s #HR #L #K #des #H elim H -L -K -des
+[ #L #T #U #H #HT <(lifts_inv_nil … H) -H //
+| #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2
+  elim (lifts_inv_cons … H) -H /3 width=10 by/
+]
+qed.
+
+lemma l1_liftables_liftables_all: ∀R,s. l_liftables1 R s → l_liftables1_all R s.
+#R #s #HR #L #K #des #HLK #Ts #Us #H elim H -Ts -Us normalize //
+#Ts #Us #T #U #HTU #_ #IHTUs * /3 width=7 by conj/
+qed.
+
 (* Basic_1: removed theorems 1: drop1_getl_trans *)