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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/notation/relations/btpred_7.ma".
16 include "basic_2/s_transition/fquq.ma".
17 include "basic_2/rt_transition/lfpr_lfpx.ma".
19 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
21 (* Basic_2A1: includes: fpbq_lleq *)
22 inductive fpbq (h) (G1) (L1) (T1): relation3 genv lenv term ≝
23 | fpbq_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h G1 L1 T1 G2 L2 T2
24 | fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → fpbq h G1 L1 T1 G1 L1 T2
25 | fpbq_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → fpbq h G1 L1 T1 G1 L2 T1
29 "parallel rst-transition (closure)"
30 'BTPRed h G1 L1 T1 G2 L2 T2 = (fpbq h G1 L1 T1 G2 L2 T2).
32 (* Basic properties *********************************************************)
34 lemma fpbq_refl: ∀h. tri_reflexive … (fpbq h).
35 /2 width=1 by fpbq_cpx/ qed.
37 (* Basic_2A1: includes: cpr_fpbq *)
38 lemma cpm_fpbq: ∀n,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L, T1⦄ ≽[h] ⦃G, L, T2⦄.
39 /3 width=2 by fpbq_cpx, cpm_fwd_cpx/ qed.
41 lemma lfpr_fpbq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L1, T⦄ ≽[h] ⦃G, L2, T⦄.
42 /3 width=1 by fpbq_lfpx, lfpr_fwd_lfpx/ qed.
44 (* Basic_2A1: removed theorems 2:
45 fpbq_fpbqa fpbqa_inv_fpbq