include "ground/lib/star.ma".
include "basic_2/notation/relations/predsubtystar_6.ma".
+include "static_2/static/reqx.ma".
include "basic_2/rt_transition/fpbq.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
(* Basic_2A1: uses: lleq_fpbs fleq_fpbs *)
lemma feqx_fpbs:
- â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â\89\9b ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+ â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â\89\85 ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
/3 width=1 by fpbq_fpbs, fpbq_feqx/ qed.
(* Basic_2A1: uses: fpbs_lleq_trans *)
lemma fpbs_feqx_trans:
∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
- â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« â\89\9b ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+ â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« â\89\85 ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
/3 width=9 by fpbs_strap1, fpbq_feqx/ qed-.
(* Basic_2A1: uses: lleq_fpbs_trans *)
lemma feqx_fpbs_trans:
∀G,G2,L,L2,T,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
- â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â\89\9b ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+ â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â\89\85 ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
/3 width=5 by fpbs_strap2, fpbq_feqx/ qed-.
lemma teqx_reqx_lpx_fpbs:
- â\88\80T1,T2. T1 â\89\9b T2 â\86\92 â\88\80L1,L0. L1 â\89\9b[T2] L0 →
+ â\88\80T1,T2. T1 â\89\85 T2 â\86\92 â\88\80L1,L0. L1 â\89\85[T2] L0 →
∀G,L2. ❪G,L0❫ ⊢ ⬈ L2 → ❪G,L1,T1❫ ≥ ❪G,L2,T2❫.
-/4 width=5 by feqx_fpbs, fpbs_strap1, fpbq_lpx, feqx_intro_dx/ qed.
+/4 width=5 by feqx_fpbs, fpbs_strap1, fpbq_lpx, feqg_intro_dx/ qed.
(* Basic_2A1: removed theorems 3:
fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs