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 f741b3e5abab35fcdc61cfc13e631d5ba976b382..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
@@ -20,34 +20,34 @@ include "basic_2/relocation/lifts_vector.ma".
 (* Main properties **********************************************************)
 
 (* Basic_1: includes: lifts_inj *)
-theorem liftsv_inj: ∀T1c,Us,f. ⬆*[f] T1c ≡ Us →
-                    ∀T2c. ⬆*[f] T2c ≡ Us → T1c = T2c.
-#T1c #Us #f #H elim H -T1c -Us
-[ #T2c #H >(liftsv_inv_nil2 … H) -H //
-| #T1c #Us #T1 #U #HT1U #_ #IHT1Us #X #H destruct
-  elim (liftsv_inv_cons2 … H) -H #T2 #T2c #HT2U #HT2Us #H destruct
+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
   >(lifts_inj … HT1U … HT2U) -U /3 width=1 by eq_f/
 ]
 qed-.
 
 (* Basic_2A1: includes: liftv_mono *)
-theorem liftsv_mono: ∀Ts,U1c,f. ⬆*[f] Ts ≡ U1c →
-                     ∀U2c. ⬆*[f] Ts ≡ U2c → U1c = U2c.
-#Ts #U1c #f #H elim H -Ts -U1c
-[ #U2c #H >(liftsv_inv_nil1 … H) -H //
-| #Ts #U1c #T #U1 #HTU1 #_ #IHTU1c #X #H destruct
-  elim (liftsv_inv_cons1 … H) -H #U2 #U2c #HTU2 #HTU2c #H destruct
+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
   >(lifts_mono … HTU1 … HTU2) -T /3 width=1 by eq_f/
 ]
 qed-.
 
 (* Basic_1: includes: lifts1_xhg (right to left) *)
 (* Basic_2A1: includes: liftsv_liftv_trans_le *)
-theorem liftsv_trans: ∀T1c,Ts,f1. ⬆*[f1] T1c ≡ Ts → ∀T2c,f2. ⬆*[f2] Ts ≡ T2c →
-                      â\88\80f. f2 â\8a\9a f1 â\89¡ f â\86\92 â¬\86*[f] T1c â\89¡ T2c.
-#T1c #Ts #f1 #H elim H -T1c -Ts
-[ #T2c #f2 #H >(liftsv_inv_nil1 … H) -T2c /2 width=3 by liftsv_nil/
-| #T1c #Ts #T1 #T #HT1 #_ #IHT1c #X #f2 #H elim (liftsv_inv_cons1 … H) -H
-  #T2 #T2c #HT2 #HT2c #H destruct /3 width=6 by lifts_trans, liftsv_cons/
+theorem liftsv_trans: ∀f1,T1s,Ts. ⬆*[f1] T1s ≘ Ts → ∀T2s,f2. ⬆*[f2] Ts ≘ T2s →
+                      â\88\80f. f2 â\8a\9a f1 â\89\98 f â\86\92 â¬\86*[f] T1s â\89\98 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-.