1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/s_transition/fqu_tdeq.ma".
16 include "static_2/static/fdeq.ma".
17 include "basic_2/rt_transition/fpb_rdeq.ma".
19 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
21 (* Properties with degree-based equivalence for closures ********************)
23 (* Basic_2A1: uses: fleq_fpb_trans *)
24 lemma fdeq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≛[h, o] ⦃F2, K2, T2⦄ →
25 ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
26 ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄.
27 #h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
28 #K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
29 elim (tdeq_fpb_trans … HT12 … H12) -T2 #K0 #T0 #H #HT0 #HK0
30 elim (rdeq_fpb_trans … HK12 … H) -K2 #L0 #U0 #H #HUT0 #HLK0
31 @(ex2_3_intro … H) -H (**) (* full auto too slow *)
32 /4 width=3 by fdeq_intro_dx, rdeq_trans, tdeq_rdeq_conf, tdeq_trans/
35 (* Inversion lemmas with degree-based equivalence for closures **************)
37 (* Basic_2A1: uses: fpb_inv_fleq *)
38 lemma fpb_inv_fdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
39 ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
40 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
41 [ #G2 #L2 #T2 #H12 #H elim (fdeq_inv_gen_sn … H) -H
42 /3 width=11 by rdeq_fwd_length, fqu_inv_tdeq/
43 | #T2 #_ #HnT #H elim (fdeq_inv_gen_sn … H) -H /2 width=1 by/
44 | #L2 #_ #HnL #H elim (fdeq_inv_gen_sn … H) -H /2 width=1 by/