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

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  14
  15 include "basic_2/rt_transition/cpx_reqg.ma".
  16 include "basic_2/rt_computation/cpxs_teqg.ma".
  17
  18 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
  19
  20 (* Properties with generic equivalence for local environments ***************)
  21
  22 (* Basic_2A1: was just: lleq_cpxs_trans *)
  23 lemma reqg_cpxs_trans (S) (G):
  24       reflexive … S → symmetric … S →
  25       ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L2 ≛[S,T0] L0 → ❪G,L2❫ ⊢ T0 ⬈* T1.
  26 #S #G #H1S #H2S #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 //
  27 #T0 #T #H0T0 #_ #IH #L2 #HL2
  28 lapply (reqg_cpx_trans … HL2 … H0T0) // #H2T0
  29 lapply (IH L2 ?) -IH /2 width=5 by cpx_reqg_conf_dx/ -L0 #H2T1
  30 /2 width=3 by cpxs_strap2/
  31 qed-.
  32
  33 (* Basic_2A1: was just: cpxs_lleq_conf *)
  34 lemma cpxs_reqg_conf (S) (G):
  35       reflexive … S → symmetric … S →
  36       ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L0 ≛[S,T0] L2 → ❪G,L2❫ ⊢ T0 ⬈* T1.
  37 /3 width=8 by reqg_cpxs_trans, reqg_sym/ qed-.
  38
  39 (* Basic_2A1: was just: lleq_conf_sn *)
  40 lemma cpxs_reqg_conf_sn (S) (G):
  41       ∀L1,T1,T2. ❪G,L1❫ ⊢ T1 ⬈* T2 →
  42       ∀L2. L1 ≛[S,T1] L2 → L1 ≛[S,T2] L2.
  43 #S #G #L1 #T1 #T2 #H @(cpxs_ind … H) -T2
  44 /3 width=6 by cpx_reqg_conf_sn/
  45 qed-.
  46
  47 (* Basic_2A1: was just: cpxs_lleq_conf_dx *)
  48 lemma cpxs_reqg_conf_dx (S) (G):
  49       reflexive … S → symmetric … S →
  50       ∀L2,T1,T2. ❪G,L2❫ ⊢ T1 ⬈* T2 →
  51       ∀L1. L1 ≛[S,T1] L2 → L1 ≛[S,T2] L2.
  52 /4 width=4 by cpxs_reqg_conf_sn, reqg_sym/ qed-.