(* Basic inversions with free variables inclusion for restricted closures ***)
lemma frees_lexs_conf: ∀R. lfxs_fsge_compatible R →
- â\88\80L1,T,f1. L1 â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f1 →
+ â\88\80L1,T,f1. L1 â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f1 →
∀L2. L1 ⪤*[cext2 R, cfull, f1] L2 →
- â\88\83â\88\83f2. L2 â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89¡ f2 & f2 ⊆ f1.
+ â\88\83â\88\83f2. L2 â\8a¢ ð\9d\90\85*â¦\83Tâ¦\84 â\89\98 f2 & f2 ⊆ f1.
#R #HR #L1 #T #f1 #Hf1 #L2 #H1L
lapply (HR L1 L2 T ?) /2 width=3 by ex2_intro/ #H2L
@(fsle_frees_trans_eq … H2L … Hf1) /3 width=4 by lexs_fwd_length, sym_eq/
qed-.
theorem lfxs_trans_fsle: ∀R1,R2,R3.
- lfxs_fsle_compatible R1 → lfxs_transitive_next R1 R2 R3 →
+ lfxs_fsle_compatible R1 → f_transitive_next R1 R2 R3 →
∀L1,L,T. L1 ⪤*[R1, T] L →
∀L2. L ⪤*[R2, T] L2 → L1 ⪤*[R3, T] L2.
#R1 #R2 #R3 #H1R #H2R #L1 #L #T #H