renaming in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_vector.ma
index fb5953c267baa16fb83b74c28aa49544e1c792be..26a4fbede90f17f51593738d9dffeff67f250d68 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_vector.ma
@@ -15,14 +15,14 @@
 include "basic_2/relocation/lifts_lifts.ma".
 include "basic_2/relocation/lifts_vector.ma".
 
-(* GENERIC TERM VECTOR RELOCATION *******************************************)
+(* GENERIC RELOCATION FOR TERM VECTORS *************************************)
 
 (* Main properties **********************************************************)
 
 (* Basic_1: includes: lifts_inj *)
-theorem liftsv_inj: ∀T1s,Us,t. ⬆*[t] T1s ≡ Us →
-                    ∀T2s. ⬆*[t] T2s ≡ Us → T1s = T2s.
-#T1s #Us #t #H elim H -T1s -Us
+theorem liftsv_inj: ∀f,T1s,Us. ⬆*[f] T1s ≘ Us →
+                    ∀T2s. ⬆*[f] T2s ≘ Us → T1s = T2s.
+#f #T1s #Us #H elim H -T1s -Us
 [ #T2s #H >(liftsv_inv_nil2 … H) -H //
 | #T1s #Us #T1 #U #HT1U #_ #IHT1Us #X #H destruct
   elim (liftsv_inv_cons2 … H) -H #T2 #T2s #HT2U #HT2Us #H destruct
@@ -31,9 +31,9 @@ theorem liftsv_inj: ∀T1s,Us,t. ⬆*[t] T1s ≡ Us →
 qed-.
 
 (* Basic_2A1: includes: liftv_mono *)
-theorem liftsv_mono: ∀Ts,U1s,t. ⬆*[t] Ts ≡ U1s →
-                     ∀U2s. ⬆*[t] Ts ≡ U2s → U1s = U2s.
-#Ts #U1s #t #H elim H -Ts -U1s
+theorem liftsv_mono: ∀f,Ts,U1s. ⬆*[f] Ts ≘ U1s →
+                     ∀U2s. ⬆*[f] Ts ≘ U2s → U1s = U2s.
+#f #Ts #U1s #H elim H -Ts -U1s
 [ #U2s #H >(liftsv_inv_nil1 … H) -H //
 | #Ts #U1s #T #U1 #HTU1 #_ #IHTU1s #X #H destruct
   elim (liftsv_inv_cons1 … H) -H #U2 #U2s #HTU2 #HTU2s #H destruct
@@ -43,11 +43,11 @@ qed-.
 
 (* Basic_1: includes: lifts1_xhg (right to left) *)
 (* Basic_2A1: includes: liftsv_liftv_trans_le *)
-theorem liftsv_trans: ∀T1s,Ts,t1. ⬆*[t1] T1s ≡ Ts → ∀T2s,t2. ⬆*[t2] Ts ≡ T2s →
-                      ∀t. t2 ⊚ t1 ≡ t → ⬆*[t] T1s ≡ T2s.
-#T1s #Ts #t1 #H elim H -T1s -Ts
-[ #T2s #t2 #H >(liftsv_inv_nil1 … H) -T2s /2 width=3 by liftsv_nil/
-| #T1s #Ts #T1 #T #HT1 #_ #IHT1s #X #t2 #H elim (liftsv_inv_cons1 … H) -H
+theorem liftsv_trans: ∀f1,T1s,Ts. ⬆*[f1] T1s ≘ Ts → ∀T2s,f2. ⬆*[f2] Ts ≘ T2s →
+                      ∀f. f2 ⊚ f1 ≘ f → ⬆*[f] T1s ≘ T2s.
+#f1 #T1s #Ts #H elim H -T1s -Ts
+[ #T2s #f2 #H >(liftsv_inv_nil1 … H) -T2s /2 width=3 by liftsv_nil/
+| #T1s #Ts #T1 #T #HT1 #_ #IHT1s #X #f2 #H elim (liftsv_inv_cons1 … H) -H
   #T2 #T2s #HT2 #HT2s #H destruct /3 width=6 by lifts_trans, liftsv_cons/
 ]
 qed-.