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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/cpx_reqx.ma".
16 include "basic_2/rt_computation/cpxs_teqx.ma".
18 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
20 (* Properties with sort-irrelevant equivalence for local environments *******)
22 (* Basic_2A1: was just: lleq_cpxs_trans *)
23 lemma reqx_cpxs_trans: ∀h,G,L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈*[h] T1 →
25 ∃∃T. ❪G,L2❫ ⊢ T0 ⬈*[h] T & T ≛ T1.
26 #h #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
27 #T0 #T #HT0 #_ #IH #L2 #HL2
28 elim (reqx_cpx_trans … HL2 … HT0) #U1 #H1 #H2
29 elim (IH L2) -IH /2 width=5 by cpx_reqx_conf_dx/ -L0 #U2 #H3 #H4
30 elim (teqx_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
31 /3 width=5 by cpxs_strap2, teqx_trans, ex2_intro/
34 (* Basic_2A1: was just: cpxs_lleq_conf *)
35 lemma cpxs_reqx_conf: ∀h,G,L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈*[h] T1 →
37 ∃∃T. ❪G,L2❫ ⊢ T0 ⬈*[h] T & T ≛ T1.
38 /3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
40 (* Basic_2A1: was just: cpxs_lleq_conf_dx *)
41 lemma cpxs_reqx_conf_dx: ∀h,G,L2,T1,T2. ❪G,L2❫ ⊢ T1 ⬈*[h] T2 →
42 ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
43 #h #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
46 (* Basic_2A1: was just: lleq_conf_sn *)
47 lemma cpxs_reqx_conf_sn: ∀h,G,L1,T1,T2. ❪G,L1❫ ⊢ T1 ⬈*[h] T2 →
48 ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
49 /4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.