matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lift.ma

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  14
  15 include "Basic_2/reducibility/cnf_lift.ma".
  16 include "Basic_2/computation/acp.ma".
  17 include "Basic_2/computation/csn.ma".
  18
  19 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma csn_acp: acp cpr (eq …) (csn …).
  24 @mk_acp
  25 [ /2 width=1/
  26 | /2 width=3/
  27 | /2 width=5/
  28 | @cnf_lift
  29 ]
  30 qed.
  31
  32 lemma csn_abst: ∀L,W. L ⊢ ⬇* W → ∀I,V,T. L. ⓑ{I} V ⊢ ⬇* T → L ⊢ ⬇* ⓛW. T.
  33 #L #W #HW elim HW -W #W #_ #IHW #I #V #T #HT @(csn_ind … HT) -T #T #HT #IHT
  34 @csn_intro #X #H1 #H2
  35 elim (cpr_inv_abst1 … H1 I V) -H1
  36 #W0 #T0 #HLW0 #HLT0 #H destruct
  37 elim (eq_false_inv_tpair … H2) -H2
  38 [ /3 width=5/
  39 | -HLW0 * #H destruct /3 width=1/
  40 ]
  41 qed.
  42
  43 (* Relocation properties ****************************************************)
  44
  45 (* Basic_1: was: sn3_lift *)
  46 lemma csn_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬇* T1 →
  47                 ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → L2 ⊢ ⬇* T2.
  48 #L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
  49 @csn_intro #T #HLT2 #HT2
  50 elim (cpr_inv_lift … HL21 … HT12 … HLT2) -HLT2 #T0 #HT0 #HLT10
  51 @(IHT1 … HLT10) // -L1 -L2 #H destruct
  52 >(lift_mono … HT0 … HT12) in HT2; -T0 /2 width=1/
  53 qed.
  54
  55 (* Basic_1: was: sn3_gen_lift *)
  56 lemma csn_inv_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬇* T1 →
  57                     ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → L2 ⊢ ⬇* T2.
  58 #L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
  59 @csn_intro #T #HLT2 #HT2
  60 elim (lift_total T d e) #T0 #HT0
  61 lapply (cpr_lift … HL12 … HT21 … HT0 HLT2) -HLT2 #HLT10
  62 @(IHT1 … HLT10) // -L1 -L2 #H destruct
  63 >(lift_inj … HT0 … HT21) in HT2; -T0 /2 width=1/
  64 qed.