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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/rt_transition/fpb_lpx.ma".
16 include "basic_2/rt_computation/fpbs_feqg.ma".
18 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
20 (* Properties with extended rt-transition on full local environments *******)
22 lemma fpbs_lpx_trans (L):
23 ∀G1,G2,L1,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L,T2❫ →
24 ∀L2. ❪G2,L❫ ⊢ ⬈ L2 → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
25 /3 width=5 by fpbs_strap1, lpx_fpb/ qed-.
27 lemma teqg_reqg_lpx_fpbs (S):
28 reflexive … S → symmetric … S →
29 ∀T1,T2. T1 ≛[S] T2 → ∀L1,L0. L1 ≛[S,T2] L0 →
30 ∀G,L2. ❪G,L0❫ ⊢ ⬈ L2 → ❪G,L1,T1❫ ≥ ❪G,L2,T2❫.
31 /4 width=7 by feqg_fpbs, fpbs_strap1, lpx_fpb, feqg_intro_dx/ qed.