(* Basic_2A1: uses: fpb_lpx *)
lemma lpx_fpbc (G) (T):
- â\88\80L1,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88 L2 â\86\92 (L1 â\89\85[T] L2 â\86\92 â\8a¥) â\86\92 â\9dªG,L1,Tâ\9d« â\89» â\9dªG,L2,Tâ\9d«.
+ â\88\80L1,L2. â\9d¨G,L1â\9d© â\8a¢ â¬\88 L2 â\86\92 (L1 â\89\85[T] L2 â\86\92 â\8a¥) â\86\92 â\9d¨G,L1,Tâ\9d© â\89» â\9d¨G,L2,Tâ\9d©.
/3 width=1 by rpx_fpbc, lpx_rpx/ qed.
(* Forward lemmas with extended rt-transition for full local envs ***********)
lemma fpbc_fwd_lpx (G1) (G2) (L1) (L2) (T1) (T2):
- â\9dªG1,L1,T1â\9d« â\89» â\9dªG2,L2,T2â\9d« →
- â\88¨â\88¨ â\88\83â\88\83G,L,T. â\9dªG1,L1,T1â\9d« â¬\82 â\9dªG,L,Tâ\9d« & â\9dªG,L,Tâ\9d« â\89½ â\9dªG2,L2,T2â\9d«
- | â\88\83â\88\83T. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88 T & T1 â\89\85 T â\86\92 â\8a¥ & â\9dªG1,L1,Tâ\9d« â\89½ â\9dªG2,L2,T2â\9d«
- | â\88\83â\88\83L. â\9dªG1,L1â\9d« â\8a¢ â¬\88 L & (L1 â\89\85[T1] L â\86\92 â\8a¥) & â\9dªG1,L,T1â\9d« â\89½ â\9dªG2,L2,T2â\9d«.
+ â\9d¨G1,L1,T1â\9d© â\89» â\9d¨G2,L2,T2â\9d© →
+ â\88¨â\88¨ â\88\83â\88\83G,L,T. â\9d¨G1,L1,T1â\9d© â¬\82 â\9d¨G,L,Tâ\9d© & â\9d¨G,L,Tâ\9d© â\89½ â\9d¨G2,L2,T2â\9d©
+ | â\88\83â\88\83T. â\9d¨G1,L1â\9d© â\8a¢ T1 â¬\88 T & T1 â\89\85 T â\86\92 â\8a¥ & â\9d¨G1,L1,Tâ\9d© â\89½ â\9d¨G2,L2,T2â\9d©
+ | â\88\83â\88\83L. â\9d¨G1,L1â\9d© â\8a¢ â¬\88 L & (L1 â\89\85[T1] L â\86\92 â\8a¥) & â\9d¨G1,L,T1â\9d© â\89½ â\9d¨G2,L2,T2â\9d©.
#G1 #G2 #L1 #L2 #T1 #T2 #H
elim (fpbc_inv_gen sfull … H) -H #H12 #Hn12
elim (fpb_inv_gen … H12) -H12 #L #T #H1 #HT2 #HL2