matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpes_cpes.ma

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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/rt_computation/lprs_cpms.ma".
  16 include "basic_2/rt_equivalence/cpes_cpms.ma".
  17
  18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-EQUIVALENCE FOR TERMS **************)
  19
  20 (* Advanced forward lemmas **************************************************)
  21
  22 lemma cpes_fwd_abst_bi (h) (n1) (n2) (p1) (p2) (G) (L):
  23       ∀W1,W2,T1,T2. ❪G,L❫ ⊢ ⓛ[p1]W1.T1 ⬌*[h,n1,n2] ⓛ[p2]W2.T2 →
  24       ∧∧ p1 = p2 & ❪G,L❫ ⊢ W1 ⬌*[h,0,O] W2.
  25 #h #n1 #n2 #p1 #p2 #G #L #W1 #W2 #T1 #T2 * #X #H1 #H2
  26 elim (cpms_inv_abst_sn … H1) #W0 #X0 #HW10 #_ #H destruct
  27 elim (cpms_inv_abst_bi … H2) #H #HW20 #_ destruct
  28 /3 width=3 by cpms_div, conj/
  29 qed-.
  30
  31 (* Main properties **********************************************************)
  32
  33 theorem cpes_cpes_trans (h) (n1) (n2) (G) (L) (T):
  34         ∀T1. ❪G,L❫ ⊢ T ⬌*[h,n1,0] T1 →
  35         ∀T2. ❪G,L❫ ⊢ T1 ⬌*[h,0,n2] T2 → ❪G,L❫ ⊢ T ⬌*[h,n1,n2] T2.
  36 #h #n1 #n2 #G #L #T #T1 #HT1 #T2 * #X #HX1 #HX2
  37 lapply (cpes_cprs_trans … HT1 … HX1) -T1 #HTX
  38 lapply (cpes_cpms_div … HTX … HX2) -X //
  39 qed-.