X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_vector.ma;h=8e234a5c1039d241987b7322ccbc7201f6690427;hp=8acd0a571249d2c4332d87ccbaf016c589c53a22;hb=222044da28742b24584549ba86b1805a87def070;hpb=9be6753b7f120a4222df17d1116fe91e871f9367

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma
index 8acd0a571..8e234a5c1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_vector.ma
@@ -19,33 +19,33 @@ include "basic_2/relocation/lifts.ma".
 
 (* Basic_2A1: includes: liftv_nil liftv_cons *)
 inductive liftsv (f:rtmap): relation (list term) ≝
-| liftsv_nil : liftsv f (◊) (◊)
+| liftsv_nil : liftsv f (Ⓔ) (Ⓔ)
 | liftsv_cons: ∀T1s,T2s,T1,T2.
-               ⬆*[f] T1 ≡ T2 → liftsv f T1s T2s →
-               liftsv f (T1 @ T1s) (T2 @ T2s)
+               ⬆*[f] T1 ≘ T2 → liftsv f T1s T2s →
+               liftsv f (T1 ⨮ T1s) (T2 ⨮ T2s)
 .
 
-interpretation "uniform relocation (vector)"
+interpretation "uniform relocation (term vector)"
    'RLiftStar i T1s T2s = (liftsv (uni i) T1s T2s).
 
-interpretation "generic relocation (vector)"
+interpretation "generic relocation (term vector)"
    'RLiftStar f T1s T2s = (liftsv f T1s T2s).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact liftsv_inv_nil1_aux: ∀f,X,Y. ⬆*[f] X ≡ Y → X = ◊ → Y = ◊.
+fact liftsv_inv_nil1_aux: ∀f,X,Y. ⬆*[f] X ≘ Y → X = Ⓔ → Y = Ⓔ.
 #f #X #Y * -X -Y //
 #T1s #T2s #T1 #T2 #_ #_ #H destruct
 qed-.
 
 (* Basic_2A1: includes: liftv_inv_nil1 *)
-lemma liftsv_inv_nil1: ∀f,Y. ⬆*[f] ◊ ≡ Y → Y = ◊.
+lemma liftsv_inv_nil1: ∀f,Y. ⬆*[f] Ⓔ ≘ Y → Y = Ⓔ.
 /2 width=5 by liftsv_inv_nil1_aux/ qed-.
 
-fact liftsv_inv_cons1_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≡ Y →
-                           ∀T1,T1s. X = T1 @ T1s →
-                           ∃∃T2,T2s. ⬆*[f] T1 ≡ T2 & ⬆*[f] T1s ≡ T2s &
-                                     Y = T2 @ T2s.
+fact liftsv_inv_cons1_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≘ Y →
+                           ∀T1,T1s. X = T1 ⨮ T1s →
+                           ∃∃T2,T2s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s &
+                                     Y = T2 ⨮ T2s.
 #f #X #Y * -X -Y
 [ #U1 #U1s #H destruct
 | #T1s #T2s #T1 #T2 #HT12 #HT12s #U1 #U1s #H destruct /2 width=5 by ex3_2_intro/
@@ -53,37 +53,37 @@ fact liftsv_inv_cons1_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≡ Y →
 qed-.
 
 (* Basic_2A1: includes: liftv_inv_cons1 *)
-lemma liftsv_inv_cons1: ∀f:rtmap. ∀T1,T1s,Y. ⬆*[f] T1 @ T1s ≡ Y →
-                        ∃∃T2,T2s. ⬆*[f] T1 ≡ T2 & ⬆*[f] T1s ≡ T2s &
-                                  Y = T2 @ T2s.
+lemma liftsv_inv_cons1: ∀f:rtmap. ∀T1,T1s,Y. ⬆*[f] T1 ⨮ T1s ≘ Y →
+                        ∃∃T2,T2s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s &
+                                  Y = T2 ⨮ T2s.
 /2 width=3 by liftsv_inv_cons1_aux/ qed-.
 
-fact liftsv_inv_nil2_aux: ∀f,X,Y. ⬆*[f] X ≡ Y → Y = ◊ → X = ◊.
+fact liftsv_inv_nil2_aux: ∀f,X,Y. ⬆*[f] X ≘ Y → Y = Ⓔ → X = Ⓔ.
 #f #X #Y * -X -Y //
 #T1s #T2s #T1 #T2 #_ #_ #H destruct
 qed-.
 
-lemma liftsv_inv_nil2: ∀f,X. ⬆*[f] X ≡ ◊ → X = ◊.
+lemma liftsv_inv_nil2: ∀f,X. ⬆*[f] X ≘ Ⓔ → X = Ⓔ.
 /2 width=5 by liftsv_inv_nil2_aux/ qed-.
 
-fact liftsv_inv_cons2_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≡ Y →
-                           ∀T2,T2s. Y = T2 @ T2s →
-                           ∃∃T1,T1s. ⬆*[f] T1 ≡ T2 & ⬆*[f] T1s ≡ T2s &
-                                     X = T1 @ T1s.
+fact liftsv_inv_cons2_aux: ∀f:rtmap. ∀X,Y. ⬆*[f] X ≘ Y →
+                           ∀T2,T2s. Y = T2 ⨮ T2s →
+                           ∃∃T1,T1s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s &
+                                     X = T1 ⨮ T1s.
 #f #X #Y * -X -Y
 [ #U2 #U2s #H destruct
 | #T1s #T2s #T1 #T2 #HT12 #HT12s #U2 #U2s #H destruct /2 width=5 by ex3_2_intro/
 ]
 qed-.
 
-lemma liftsv_inv_cons2: ∀f:rtmap. ∀X,T2,T2s. ⬆*[f] X ≡ T2 @ T2s →
-                        ∃∃T1,T1s. ⬆*[f] T1 ≡ T2 & ⬆*[f] T1s ≡ T2s &
-                                  X = T1 @ T1s.
+lemma liftsv_inv_cons2: ∀f:rtmap. ∀X,T2,T2s. ⬆*[f] X ≘ T2 ⨮ T2s →
+                        ∃∃T1,T1s. ⬆*[f] T1 ≘ T2 & ⬆*[f] T1s ≘ T2s &
+                                  X = T1 ⨮ T1s.
 /2 width=3 by liftsv_inv_cons2_aux/ qed-.
 
 (* Basic_1: was: lifts1_flat (left to right) *)
-lemma lifts_inv_applv1: ∀f:rtmap. ∀V1s,U1,T2. ⬆*[f] Ⓐ V1s.U1 ≡ T2 →
-                        ∃∃V2s,U2. ⬆*[f] V1s ≡ V2s & ⬆*[f] U1 ≡ U2 &
+lemma lifts_inv_applv1: ∀f:rtmap. ∀V1s,U1,T2. ⬆*[f] Ⓐ V1s.U1 ≘ T2 →
+                        ∃∃V2s,U2. ⬆*[f] V1s ≘ V2s & ⬆*[f] U1 ≘ U2 &
                                   T2 = Ⓐ V2s.U2.
 #f #V1s elim V1s -V1s
 [ /3 width=5 by ex3_2_intro, liftsv_nil/
@@ -93,8 +93,8 @@ lemma lifts_inv_applv1: ∀f:rtmap. ∀V1s,U1,T2. ⬆*[f] Ⓐ V1s.U1 ≡ T2 →
 ]
 qed-.
 
-lemma lifts_inv_applv2: ∀f:rtmap. ∀V2s,U2,T1. ⬆*[f] T1 ≡ Ⓐ V2s.U2 →
-                        ∃∃V1s,U1. ⬆*[f] V1s ≡ V2s & ⬆*[f] U1 ≡ U2 &
+lemma lifts_inv_applv2: ∀f:rtmap. ∀V2s,U2,T1. ⬆*[f] T1 ≘ Ⓐ V2s.U2 →
+                        ∃∃V1s,U1. ⬆*[f] V1s ≘ V2s & ⬆*[f] U1 ≘ U2 &
                                   T1 = Ⓐ V1s.U1.
 #f #V2s elim V2s -V2s
 [ /3 width=5 by ex3_2_intro, liftsv_nil/
@@ -107,7 +107,7 @@ qed-.
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: includes: liftv_total *)
-lemma liftsv_total: ∀f. ∀T1s:list term. ∃T2s. ⬆*[f] T1s ≡ T2s.
+lemma liftsv_total: ∀f. ∀T1s:list term. ∃T2s. ⬆*[f] T1s ≘ T2s.
 #f #T1s elim T1s -T1s
 [ /2 width=2 by liftsv_nil, ex_intro/
 | #T1 #T1s * #T2s #HT12s
@@ -116,15 +116,15 @@ lemma liftsv_total: ∀f. ∀T1s:list term. ∃T2s. ⬆*[f] T1s ≡ T2s.
 qed-.
 
 (* Basic_1: was: lifts1_flat (right to left) *)
-lemma lifts_applv: ∀f:rtmap. ∀V1s,V2s. ⬆*[f] V1s ≡ V2s →
-                   ∀T1,T2. ⬆*[f] T1 ≡ T2 →
-                   ⬆*[f] Ⓐ V1s.T1 ≡ Ⓐ V2s.T2.
+lemma lifts_applv: ∀f:rtmap. ∀V1s,V2s. ⬆*[f] V1s ≘ V2s →
+                   ∀T1,T2. ⬆*[f] T1 ≘ T2 →
+                   ⬆*[f] Ⓐ V1s.T1 ≘ Ⓐ V2s.T2.
 #f #V1s #V2s #H elim H -V1s -V2s /3 width=1 by lifts_flat/
 qed.
 
-lemma liftsv_split_trans: ∀f,T1s,T2s. ⬆*[f] T1s ≡ T2s →
-                          ∀f1,f2. f2 ⊚ f1 ≡ f →
-                          ∃∃Ts. ⬆*[f1] T1s ≡ Ts & ⬆*[f2] Ts ≡ T2s.
+lemma liftsv_split_trans: ∀f,T1s,T2s. ⬆*[f] T1s ≘ T2s →
+                          ∀f1,f2. f2 ⊚ f1 ≘ f →
+                          ∃∃Ts. ⬆*[f1] T1s ≘ Ts & ⬆*[f2] Ts ≘ T2s.
 #f #T1s #T2s #H elim H -T1s -T2s
 [ /2 width=3 by liftsv_nil, ex2_intro/
 | #T1s #T2s #T1 #T2 #HT12 #_ #IH #f1 #f2 #Hf