(* Properties with extended rt-transition on full local environments *******)
lemma fpbs_lpx_trans (L):
- â\88\80G1,G2,L1,T1,T2. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L,T2â\9d« →
- â\88\80L2. â\9dªG2,Lâ\9d« â\8a¢ â¬\88 L2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,G2,L1,T1,T2. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L,T2â\9d© →
+ â\88\80L2. â\9d¨G2,Lâ\9d© â\8a¢ â¬\88 L2 â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
/3 width=5 by fpbs_strap1, lpx_fpb/ qed-.
lemma teqg_reqg_lpx_fpbs (S):
reflexive … S → symmetric … S →
∀T1,T2. T1 ≛[S] T2 → ∀L1,L0. L1 ≛[S,T2] L0 →
- â\88\80G,L2. â\9dªG,L0â\9d« â\8a¢ â¬\88 L2 â\86\92 â\9dªG,L1,T1â\9d« â\89¥ â\9dªG,L2,T2â\9d«.
+ â\88\80G,L2. â\9d¨G,L0â\9d© â\8a¢ â¬\88 L2 â\86\92 â\9d¨G,L1,T1â\9d© â\89¥ â\9d¨G,L2,T2â\9d©.
/4 width=7 by feqg_fpbs, fpbs_strap1, lpx_fpb, feqg_intro_dx/ qed.