matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma

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  14
  15 include "basic_2/rt_transition/cpx_reqx.ma".
  16 include "basic_2/rt_computation/cpxs_teqx.ma".
  17
  18 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
  19
  20 (* Properties with sort-irrelevant equivalence for local environments *******)
  21
  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/
  30 qed-.
  31
  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-.
  36
  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/
  42 qed-.
  43
  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-.