include "basic_2/notation/relations/predsubtyproper_7.ma".
include "static_2/s_transition/fqu.ma".
-include "static_2/static/rdeq.ma".
+include "static_2/static/reqx.ma".
include "basic_2/rt_transition/lpr_lpx.ma".
(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
inductive fpb (h) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpb_fqu: â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\8a\90 â¦\83G2,L2,T2â¦\84 → fpb h G1 L1 T1 G2 L2 T2
-| fpb_cpx: â\88\80T2. â¦\83G1,L1â¦\84 ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → fpb h G1 L1 T1 G1 L1 T2
-| fpb_lpx: â\88\80L2. â¦\83G1,L1â¦\84 ⊢ ⬈[h] L2 → (L1 ≛[T1] L2 → ⊥) → fpb h G1 L1 T1 G1 L2 T1
+| fpb_fqu: â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â¬\82 â\9dªG2,L2,T2â\9d« → fpb h G1 L1 T1 G2 L2 T2
+| fpb_cpx: â\88\80T2. â\9dªG1,L1â\9d« ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → fpb h G1 L1 T1 G1 L1 T2
+| fpb_lpx: â\88\80L2. â\9dªG1,L1â\9d« ⊢ ⬈[h] L2 → (L1 ≛[T1] L2 → ⊥) → fpb h G1 L1 T1 G1 L2 T1
.
interpretation
(* Basic properties *********************************************************)
(* Basic_2A1: includes: cpr_fpb *)
-lemma cpm_fpb (n) (h) (G) (L): â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ➡[n,h] T2 → (T1 ≛ T2 → ⊥) →
- â¦\83G,L,T1â¦\84 â\89»[h] â¦\83G,L,T2â¦\84.
+lemma cpm_fpb (n) (h) (G) (L): â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡[n,h] T2 → (T1 ≛ T2 → ⊥) →
+ â\9dªG,L,T1â\9d« â\89»[h] â\9dªG,L,T2â\9d«.
/3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
-lemma lpr_fpb (h) (G) (T): â\88\80L1,L2. â¦\83G,L1â¦\84 ⊢ ➡[h] L2 → (L1 ≛[T] L2 → ⊥) →
- â¦\83G,L1,Tâ¦\84 â\89»[h] â¦\83G,L2,Tâ¦\84.
+lemma lpr_fpb (h) (G) (T): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡[h] L2 → (L1 ≛[T] L2 → ⊥) →
+ â\9dªG,L1,Tâ\9d« â\89»[h] â\9dªG,L2,Tâ\9d«.
/3 width=1 by fpb_lpx, lpr_fwd_lpx/ qed.