(* Advanced forward lemmas **************************************************)
lemma fpbg_fwd_fpbs (G1) (G2) (L1) (L2) (T1) (T2):
- â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+ â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
#G1 #G2 #L1 #L2 #T1 #T2 #H
elim (fpbg_inv_gen … H) -H
/4 width=9 by fpbs_trans, fpbs_strap2, fpbc_fwd_fpb/
(* Advanced properties ******************************************************)
lemma fpbs_fpbg_trans (G) (L) (T):
- â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG,L,Tâ\9d« →
- â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« > â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,L1,T1. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G,L,Tâ\9d© →
+ â\88\80G2,L2,T2. â\9d¨G,L,Tâ\9d© > â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d©.
#G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
elim (fpbg_inv_gen … H2) -H2
/3 width=13 by fpbg_intro, fpbs_trans/
(* Note: this is used in the closure proof *)
lemma fpbg_fpbs_trans (G) (L) (T):
- â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« > â\9dªG,L,Tâ\9d« →
- â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« â\89¥ â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« > â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,L1,T1. â\9d¨G1,L1,T1â\9d© > â\9d¨G,L,Tâ\9d© →
+ â\88\80G2,L2,T2. â\9d¨G,L,Tâ\9d© â\89¥ â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d©.
#G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
elim (fpbg_inv_gen … H1) -H1
/3 width=13 by fpbg_intro, fpbs_trans/