(* Basic_2A1: was: cpxs_fpbg *)
lemma cpxs_tneqx_fpbg:
- â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 →
- (T1 â\89\85 T2 â\86\92 â\8a¥) â\86\92 â\9dªG,L,T1â\9d« > â\9dªG,L,T2â\9d«.
+ â\88\80G,L,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 →
+ (T1 â\89\85 T2 â\86\92 â\8a¥) â\86\92 â\9d¨G,L,T1â\9d© > â\9d¨G,L,T2â\9d©.
#G #L #T1 #T2 #H #H0
elim (cpxs_tneqg_fwd_step_sn … H … H0) -H -H0
/4 width=5 by fpbc_fpbs_fpbg, cpxs_fpbs, cpx_fpbc, sfull_dec/
qed.
lemma cpxs_fpbg_trans:
- â\88\80G1,L1,T1,T. â\9dªG1,L1â\9d« ⊢ T1 ⬈* T →
- â\88\80G2,L2,T2. â\9dªG1,L1,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,T. â\9d¨G1,L1â\9d© ⊢ T1 ⬈* T →
+ â\88\80G2,L2,T2. â\9d¨G1,L1,Tâ\9d© > â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© > â\9d¨G2,L2,T2â\9d©.
/3 width=5 by fpbs_fpbg_trans, cpxs_fpbs/ qed-.