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15 include "basic_2/static/ffdeq.ma".
16 include "basic_2/rt_transition/fpb_lfdeq.ma".
18 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
20 (* Properties with degree-based equivalence for closures ********************)
22 (* Basic_2A1: uses: fleq_fpb_trans *)
23 lemma ffdeq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≛[h, o] ⦃F2, K2, T2⦄ →
24 ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
25 ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄.
26 #h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
27 #K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
28 elim (tdeq_fpb_trans … HT12 … H12) -T2 #K0 #T0 #H #HT0 #HK0
29 elim (lfdeq_fpb_trans … HK12 … H) -K2 #L0 #U0 #H #HUT0 #HLK0
30 @(ex2_3_intro … H) -H (**) (* full auto too slow *)
31 /4 width=3 by ffdeq_intro_dx, lfdeq_trans, tdeq_lfdeq_conf, tdeq_trans/
34 (* Inversion lemmas with degree-based equivalence for closures **************)
36 (* Basic_2A1: uses: fpb_inv_fleq *)
37 lemma fpb_inv_ffdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
38 ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
39 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
40 [ #G2 #L2 #T2 #H12 #H elim (ffdeq_inv_gen_sn … H) -H
44 /3 width=8 by lfdeq_fwd_length, fqu_inv_eq/
46 | #T2 #_ #HnT #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
47 | #L2 #_ #HnL #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/