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_7.ma".
16 include "static_2/s_transition/fqu.ma".
17 include "static_2/static/reqx.ma".
18 include "basic_2/rt_transition/lpr_lpx.ma".
20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
22 inductive fpb (h) (G1) (L1) (T1): relation3 genv lenv term ≝
23 | fpb_fqu: ∀G2,L2,T2. ❪G1,L1,T1❫ ⬂ ❪G2,L2,T2❫ → fpb h G1 L1 T1 G2 L2 T2
24 | fpb_cpx: ∀T2. ❪G1,L1❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → fpb h G1 L1 T1 G1 L1 T2
25 | fpb_lpx: ∀L2. ❪G1,L1❫ ⊢ ⬈[h] L2 → (L1 ≛[T1] L2 → ⊥) → fpb h G1 L1 T1 G1 L2 T1
29 "proper parallel rst-transition (closure)"
30 'PRedSubTyProper h G1 L1 T1 G2 L2 T2 = (fpb h G1 L1 T1 G2 L2 T2).
32 (* Basic properties *********************************************************)
34 (* Basic_2A1: includes: cpr_fpb *)
35 lemma cpm_fpb (n) (h) (G) (L): ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[n,h] T2 → (T1 ≛ T2 → ⊥) →
36 ❪G,L,T1❫ ≻[h] ❪G,L,T2❫.
37 /3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
39 lemma lpr_fpb (h) (G) (T): ∀L1,L2. ❪G,L1❫ ⊢ ➡[h] L2 → (L1 ≛[T] L2 → ⊥) →
40 ❪G,L1,T❫ ≻[h] ❪G,L2,T❫.
41 /3 width=1 by fpb_lpx, lpr_fwd_lpx/ qed.