(* Main properties **********************************************************)
(* Basic_1: includes: lifts_inj *)
-theorem liftsv_inj: â\88\80f,T1s,Us. â¬\86*[f] T1s â\89¡ Us →
- â\88\80T2s. â¬\86*[f] T2s â\89¡ Us → T1s = T2s.
+theorem liftsv_inj: â\88\80f,T1s,Us. â¬\86*[f] T1s â\89\98 Us →
+ â\88\80T2s. â¬\86*[f] T2s â\89\98 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
qed-.
(* Basic_2A1: includes: liftv_mono *)
-theorem liftsv_mono: â\88\80f,Ts,U1s. â¬\86*[f] Ts â\89¡ U1s →
- â\88\80U2s. â¬\86*[f] Ts â\89¡ U2s → U1s = U2s.
+theorem liftsv_mono: â\88\80f,Ts,U1s. â¬\86*[f] Ts â\89\98 U1s →
+ â\88\80U2s. â¬\86*[f] Ts â\89\98 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
(* Basic_1: includes: lifts1_xhg (right to left) *)
(* Basic_2A1: includes: liftsv_liftv_trans_le *)
-theorem liftsv_trans: â\88\80f1,T1s,Ts. â¬\86*[f1] T1s â\89¡ Ts â\86\92 â\88\80T2s,f2. â¬\86*[f2] Ts â\89¡ T2s →
- â\88\80f. f2 â\8a\9a f1 â\89¡ f â\86\92 â¬\86*[f] T1s â\89¡ T2s.
+theorem liftsv_trans: â\88\80f1,T1s,Ts. â¬\86*[f1] T1s â\89\98 Ts â\86\92 â\88\80T2s,f2. â¬\86*[f2] Ts â\89\98 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