(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
definition lfxs (R) (T): relation lenv ≝
- λL1,L2. â\88\83â\88\83f. L1 â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f & L1 ⪤*[cext2 R, cfull, f] L2.
+ λL1,L2. â\88\83â\88\83f. L1 â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f & L1 ⪤*[cext2 R, cfull, f] L2.
interpretation "generic extension on referred entries (local environment)"
'RelationStar R T L1 L2 = (lfxs R T L1 L2).
qed-.
lemma lfxs_isid: ∀R1,R2,L1,L2,T1,T2.
- (â\88\80f. L1 â\8a¢ ð\9d\90\85*â¦\83T1â¦\84 â\89¡ f → 𝐈⦃f⦄) →
- (â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L1 â\8a¢ ð\9d\90\85*â¦\83T2â¦\84 â\89¡ f) →
+ (â\88\80f. L1 â\8a¢ ð\9d\90\85*â¦\83T1â¦\84 â\89\98 f → 𝐈⦃f⦄) →
+ (â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L1 â\8a¢ ð\9d\90\85*â¦\83T2â¦\84 â\89\98 f) →
L1 ⪤*[R1, T1] L2 → L1 ⪤*[R2, T2] L2.
#R1 #R2 #L1 #L2 #T1 #T2 #H1 #H2 *
/4 width=7 by lexs_co_isid, ex2_intro/