update in ground_2, static_2, basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / lifts_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma
index f424d38eae4842054661e8da956375eedb2b7fe2..a5310b63dce69cde3da9653a854b652b927ea979 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts_vector.ma
@@ -18,34 +18,35 @@ include "static_2/relocation/lifts.ma".
 (* GENERIC RELOCATION FOR TERM VECTORS *************************************)
 
 (* Basic_2A1: includes: liftv_nil liftv_cons *)
-inductive liftsv (f:rtmap): relation (list term) ≝
+inductive liftsv (f): relation … ≝
 | liftsv_nil : liftsv f (Ⓔ) (Ⓔ)
 | liftsv_cons: ∀T1s,T2s,T1,T2.
                ⇧*[f] T1 ≘ T2 → liftsv f T1s T2s →
                liftsv f (T1 ⨮ T1s) (T2 ⨮ T2s)
 .
 
-interpretation "uniform relocation (term vector)"
-   'RLiftStar i T1s T2s = (liftsv (uni i) T1s T2s).
-
 interpretation "generic relocation (term vector)"
    'RLiftStar f T1s T2s = (liftsv f T1s T2s).
 
+interpretation "uniform relocation (term vector)"
+   'RLift i T1s T2s = (liftsv (uni i) 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):
+     ∀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/
@@ -53,38 +54,39 @@ 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):
+      ∀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):
+     ∀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):
+      ∀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 &
-                                  T2 = Ⓐ V2s.U2.
+lemma lifts_inv_applv1 (f):
+      ∀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/
 | #V1 #V1s #IHV1s #T1 #X #H elim (lifts_inv_flat1 … H) -H
@@ -93,9 +95,9 @@ 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 &
-                                  T1 = Ⓐ V1s.U1.
+lemma lifts_inv_applv2 (f):
+      ∀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/
 | #V2 #V2s #IHV2s #T2 #X #H elim (lifts_inv_flat2 … H) -H
@@ -107,7 +109,8 @@ qed-.
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: includes: liftv_total *)
-lemma liftsv_total: ∀f. ∀T1s:list term. ∃T2s. ⇧*[f] T1s ≘ T2s.
+lemma liftsv_total (f):
+      ∀T1s. ∃T2s. ⇧*[f] T1s ≘ T2s.
 #f #T1s elim T1s -T1s
 [ /2 width=2 by liftsv_nil, ex_intro/
 | #T1 #T1s * #T2s #HT12s
@@ -116,15 +119,15 @@ 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):
+      ∀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