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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_computation/fpbg_fqup.ma".
16 include "basic_2/rt_computation/fpbg_cpxs.ma".
17 include "basic_2/rt_computation/cpms_fpbs.ma".
19 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
21 (* Forward lemmas with proper parallel rst-computation for closures *********)
23 lemma cpms_tdneq_fwd_fpbg (h) (o) (n): ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 →
24 (T1 ≛[h,o] T2 → ⊥) → ⦃G,L,T1⦄ >[h,o] ⦃G,L,T2⦄.
25 /3 width=2 by cpms_fwd_cpxs, cpxs_tdneq_fpbg/ qed-.
27 lemma fpbg_cpms_trans (h) (o) (n): ∀G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T⦄ →
28 ∀T2. ⦃G2, L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T2⦄.
29 /3 width=5 by fpbg_fpbs_trans, cpms_fwd_fpbs/ qed-.
31 lemma cpms_fpbg_trans (h) (o) (n): ∀G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ➡*[n,h] T →
32 ∀G2,L2,T2. ⦃G1, L1, T⦄ >[h,o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T2⦄.
33 /3 width=5 by fpbs_fpbg_trans, cpms_fwd_fpbs/ qed-.
35 lemma fqup_cpms_fwd_fpbg (h) (o): ∀G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T⦄ →
36 ∀n,T2. ⦃G2, L2⦄ ⊢ T ➡*[n,h] T2 → ⦃G1, L1, T1⦄ >[h,o] ⦃G2, L2, T2⦄.
37 /3 width=5 by cpms_fwd_fpbs, fqup_fpbg,fpbg_fpbs_trans/ qed-.
39 lemma cpm_tdneq_cpm_cpms_tdeq_sym_fwd_fpbg (h) (o) (G) (L) (T1):
40 ∀n1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛[h,o] T → ⊥) →
41 ∀n2,T2. ⦃G,L⦄⊢ T ➡*[n2,h] T2 → T1 ≛[h,o] T2 → ⦃G,L,T1⦄ >[h,o] ⦃G,L,T1⦄.
42 #h #o #G #L #T1 #n1 #T #H1T1 #H2T1 #n2 #T2 #H1T2 #H2T12
43 /4 width=7 by cpms_fwd_fpbs, cpm_fpb, fpbs_tdeq_trans, tdeq_sym, ex2_3_intro/