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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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11 (* v GNU General Public License Version 2 *)
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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 → ❪G,L2❫ ⊢ T0 ⬈* T1.
25 #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 //
26 #T0 #T #H0T0 #_ #IH #L2 #HL2
27 lapply (reqx_cpx_trans … HL2 … H0T0) #H2T0
28 lapply (IH L2 ?) -IH /2 width=5 by cpx_reqx_conf_dx/ -L0 #H2T1
29 /2 width=3 by cpxs_strap2/
32 (* Basic_2A1: was just: cpxs_lleq_conf *)
33 lemma cpxs_reqx_conf (G):
34 ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L0 ≛[T0] L2 → ❪G,L2❫ ⊢ T0 ⬈* T1.
35 /3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
37 (* Basic_2A1: was just: cpxs_lleq_conf_dx *)
38 lemma cpxs_reqx_conf_dx (G):
39 ∀L2,T1,T2. ❪G,L2❫ ⊢ T1 ⬈* T2 →
40 ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
41 #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
44 (* Basic_2A1: was just: lleq_conf_sn *)
45 lemma cpxs_reqx_conf_sn (G):
46 ∀L1,T1,T2. ❪G,L1❫ ⊢ T1 ⬈* T2 →
47 ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
48 /4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.