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15 include "basic_2A/substitution/drop_lreq.ma".
16 include "basic_2A/reduction/cpx.ma".
18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
20 (* Properties on equivalence for local environments *************************)
22 lemma lreq_cpx_trans: ∀h,g,G. lsub_trans … (cpx h g G) (lreq 0 (∞)).
23 #h #g #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
25 | /2 width=2 by cpx_st/
26 | #I #G #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
27 elim (lreq_drop_trans_be … HL12 … HLK1) // -HL12 -HLK1 /3 width=7 by cpx_delta/
28 |4,9: /4 width=1 by cpx_bind, cpx_beta, lreq_pair_O_Y/
29 |5,7,8: /3 width=1 by cpx_flat, cpx_eps, cpx_ct/
30 |6,10: /4 width=3 by cpx_zeta, cpx_theta, lreq_pair_O_Y/