(* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
definition s_rs_transitive_isid: relation (relation3 lenv bind bind) ≝ λRN,RP.
- â\88\80f. ð\9d\90\88â\9dªfâ\9d« → s_rs_transitive … RP (λ_.sex RN RP f).
+ â\88\80f. ð\9d\90\88â\9d¨fâ\9d© → s_rs_transitive … RP (λ_.sex RN RP f).
(* Properties with transitive closure ***************************************)
(* Basic_2A1: uses: TC_lpx_sn_ind *)
theorem sex_tc_step_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
- â\88\80f,L1,L. L1 ⪤[RN,RP,f] L â\86\92 ð\9d\90\88â\9dªfâ\9d« →
+ â\88\80f,L1,L. L1 ⪤[RN,RP,f] L â\86\92 ð\9d\90\88â\9d¨fâ\9d© →
∀L2. L ⪤[RN,CTC … RP,f] L2 → L1⪤ [RN,CTC … RP,f] L2.
#RN #RP #HRP #f #L1 #L #H elim H -f -L1 -L
[ #f #_ #Y #H -HRP >(sex_inv_atom1 … H) -Y // ]
(* Advanced properties ******************************************************)
lemma sex_tc_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
- â\88\80f. ð\9d\90\88â\9dªfâ\9d« → ∀L1,L2. TC … (sex RN RP f) L1 L2 → L1 ⪤[RN,CTC … RP,f] L2.
+ â\88\80f. ð\9d\90\88â\9d¨fâ\9d© → ∀L1,L2. TC … (sex RN RP f) L1 L2 → L1 ⪤[RN,CTC … RP,f] L2.
#RN #RP #HRP #f #Hf #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
/3 width=3 by sex_tc_step_dx, sex_tc_inj_dx/
qed.