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15 include "static_2/static/fdeq.ma".
16 include "basic_2/rt_transition/cpx_rdeq.ma".
17 include "basic_2/rt_transition/rpx_rdeq.ma".
19 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
21 (* Properties with degree-based equivalence for closures ********************)
23 lemma fdeq_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T⦄ →
24 ∀T2. ⦃G2, L2⦄ ⊢ T ⬈[h] T2 →
25 ∃∃T0. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T0 & ⦃G1, L1, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
26 #h #o #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
27 elim (fdeq_inv_gen_dx … H) -H #H #HL12 #HT1 destruct
28 elim (rdeq_cpx_trans … HL12 … HT2) #T0 #HT0 #HT02
29 lapply (cpx_rdeq_conf_dx … HT2 … HL12) -HL12 #HL12
30 elim (tdeq_cpx_trans … HT1 … HT0) -T #T #HT1 #HT0
31 /4 width=5 by fdeq_intro_dx, tdeq_trans, ex2_intro/