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 "basic_2/notation/relations/predsubtyproper_8.ma".
16 include "basic_2/s_transition/fqu.ma".
17 include "basic_2/static/lfdeq.ma".
18 include "basic_2/rt_transition/lfpr_lfpx.ma".
20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
22 inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
23 | fpb_fqu : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2
24 | fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2
25 | fpb_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → (L1 ≛[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1
29 "proper parallel rst-transition (closure)"
30 'PRedSubTyProper h o G1 L1 T1 G2 L2 T2 = (fpb h o G1 L1 T1 G2 L2 T2).
32 (* Basic properties *********************************************************)
34 (* Basic_2A1: includes: cpr_fpb *)
35 lemma cpm_fpb: ∀n,h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → (T1 ≛[h, o] T2 → ⊥) →
36 ⦃G, L, T1⦄ ≻[h, o] ⦃G, L, T2⦄.
37 /3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
39 (* Basic_2A1: includes: lpr_fpb *)
40 lemma lfpr_fpb: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → (L1 ≛[h, o, T] L2 → ⊥) →
41 ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄.
42 /3 width=1 by fpb_lfpx, lfpr_fwd_lfpx/ qed.