(* *)
(**************************************************************************)
-include "basic_2/notation/relations/btpred_7.ma".
+include "basic_2/notation/relations/predsubty_8.ma".
+include "basic_2/static/ffdeq.ma".
include "basic_2/s_transition/fquq.ma".
include "basic_2/rt_transition/lfpr_lfpx.ma".
(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
(* Basic_2A1: includes: fpbq_lleq *)
-inductive fpbq (h) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpbq_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h G1 L1 T1 G2 L2 T2
-| fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → fpbq h G1 L1 T1 G1 L1 T2
-| fpbq_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → fpbq h G1 L1 T1 G1 L2 T1
+inductive fpbq (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
+| fpbq_fquq : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h o G1 L1 T1 G2 L2 T2
+| fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → fpbq h o G1 L1 T1 G1 L1 T2
+| fpbq_lfpx : ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → fpbq h o G1 L1 T1 G1 L2 T1
+| ffpq_lfdeq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → fpbq h o G1 L1 T1 G2 L2 T2
.
interpretation
"parallel rst-transition (closure)"
- 'BTPRed h G1 L1 T1 G2 L2 T2 = (fpbq h G1 L1 T1 G2 L2 T2).
+ 'PRedSubTy h o G1 L1 T1 G2 L2 T2 = (fpbq h o G1 L1 T1 G2 L2 T2).
(* Basic properties *********************************************************)
-lemma fpbq_refl: ∀h. tri_reflexive … (fpbq h).
+lemma fpbq_refl: ∀h,o. tri_reflexive … (fpbq h o).
/2 width=1 by fpbq_cpx/ qed.
(* Basic_2A1: includes: cpr_fpbq *)
-lemma cpm_fpbq: ∀n,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L, T1⦄ ≽[h] ⦃G, L, T2⦄.
+lemma cpm_fpbq: ∀n,h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L, T1⦄ ≽[h, o] ⦃G, L, T2⦄.
/3 width=2 by fpbq_cpx, cpm_fwd_cpx/ qed.
-lemma lfpr_fpbq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L1, T⦄ ≽[h] ⦃G, L2, T⦄.
+lemma lfpr_fpbq: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L1, T⦄ ≽[h, o] ⦃G, L2, T⦄.
/3 width=1 by fpbq_lfpx, lfpr_fwd_lfpx/ qed.
(* Basic_2A1: removed theorems 2: