matita/matita/contribs/lambdadelta/basic_2A/computation/cpxs_lleq.ma

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  14
  15 include "basic_2A/reduction/cpx_lleq.ma".
  16 include "basic_2A/computation/cpxs.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
  19
  20 (* Properties on lazy equivalence for local environments ********************)
  21
  22 lemma lleq_cpxs_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
  23                        ∀L1. L1 ≡[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2.
  24 #h #g #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1
  25 /4 width=6 by cpx_lleq_conf_dx, lleq_cpx_trans, cpxs_strap2/
  26 qed-.
  27
  28 lemma cpxs_lleq_conf: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
  29                       ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2.
  30 /3 width=3 by lleq_cpxs_trans, lleq_sym/ qed-.
  31
  32 lemma cpxs_lleq_conf_dx: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
  33                          ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
  34 #h #g #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lleq_conf_dx/
  35 qed-.
  36
  37 lemma cpxs_lleq_conf_sn: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2 →
  38                          ∀L2. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
  39 /4 width=6 by cpxs_lleq_conf_dx, lleq_sym/ qed-.