X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_lifts_vector.ma;h=26a4fbede90f17f51593738d9dffeff67f250d68;hp=6093315abe83662f3d7bde7b7bdd7c77c73bc2c3;hb=222044da28742b24584549ba86b1805a87def070;hpb=e9da8e091898b6e67a2f270581bdc5cdbe80e9b0

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 6093315ab..26a4fbede 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_vector.ma
@@ -20,8 +20,8 @@ include "basic_2/relocation/lifts_vector.ma".
 (* Main properties **********************************************************)
 
 (* Basic_1: includes: lifts_inj *)
-theorem liftsv_inj: ∀f,T1s,Us. ⬆*[f] T1s ≡ Us →
-                    ∀T2s. ⬆*[f] T2s ≡ Us → T1s = T2s.
+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
@@ -31,8 +31,8 @@ theorem liftsv_inj: ∀f,T1s,Us. ⬆*[f] T1s ≡ Us →
 qed-.
 
 (* Basic_2A1: includes: liftv_mono *)
-theorem liftsv_mono: ∀f,Ts,U1s. ⬆*[f] Ts ≡ U1s →
-                     ∀U2s. ⬆*[f] Ts ≡ U2s → U1s = U2s.
+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
@@ -43,8 +43,8 @@ qed-.
 
 (* Basic_1: includes: lifts1_xhg (right to left) *)
 (* Basic_2A1: includes: liftsv_liftv_trans_le *)
-theorem liftsv_trans: ∀f1,T1s,Ts. ⬆*[f1] T1s ≡ Ts → ∀T2s,f2. ⬆*[f2] Ts ≡ T2s →
-                      ∀f. f2 ⊚ f1 ≡ f → ⬆*[f] T1s ≡ T2s.
+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