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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/rt_transition/cpx_reqx.ma".
16 include "basic_2/rt_computation/cpxs_teqx.ma".
18 (* EXTENDED 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 (G):
24 ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L2 ≛[T0] L0 →
25 ∃∃T. ❪G,L2❫ ⊢ T0 ⬈* T & T ≛ T1.
26 #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 (G):
36 ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L0 ≛[T0] L2 →
37 ∃∃T. ❪G,L2❫ ⊢ T0 ⬈* 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 (G):
42 ∀L2,T1,T2. ❪G,L2❫ ⊢ T1 ⬈* T2 →
43 ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
44 #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
47 (* Basic_2A1: was just: lleq_conf_sn *)
48 lemma cpxs_reqx_conf_sn (G):
49 ∀L1,T1,T2. ❪G,L1❫ ⊢ T1 ⬈* T2 →
50 ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
51 /4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.