matita/matita/contribs/lambdadelta/apps_2/etc/models/model_cpr.etc

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  14
  15 include "basic_2/reduction/cpr.ma".
  16 include "apps_2/models/model_drop.ma".
  17
  18 (* MODEL ********************************************************************)
  19
  20 (* Forward lemmas on context-sensitive parallel reduction for terms *********)
  21
  22 lemma sound_fwd_cpr: ∀M. sound M → extensional M →
  23                      ∀sv,gv,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 →
  24                      ∀lv. lv ∈ 〚L〛⦋M⦌{sv, gv} → 〚T1〛{sv, gv, lv} = 〚T2〛{sv, gv, lv}.
  25 #M #H1M #H2M #sv #gv #G #L #T1 #T2 #H elim H -G -L -T1 -T2 //
  26 [ #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #lv #Hlv >(m2 … H1M)
  27   <(sound_fwd_lift … H1M H2M … HVW2) -HVW2
  28   lapply (sound_drop … HLK … Hlv) // -L -H2M #H
  29   elim (li_inv_ldef … H) -H #v #HK #H
  30   elim (lower_inv_raise_be … H) -H #H >H -H #Hlv
  31   <IHV12 -IHV12 /3 width=3 by sound_ti_eq_l, li_veq, veq_sym/
  32 | #a * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #lv #Hlv
  33   [ >(m4 … H1M) >(m4 … H1M) -H1M <IHV12 -IHV12 /3 width=1 by li_ldef/
  34   | @(mx … H2M) -H2M /3 width=1 by li_ldec/
  35   ]
  36 | * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #lv #Hlv
  37   [ >(m6 … H1M) >(m6 … H1M) -H1M /3 width=1 by eq_f2/
  38   | -IHV12 >(m7 … H1M) >(m7 … H1M) -H1M /2 width=1 by/
  39   ]
  40 | #G #L #V #U1 #U2 #T2 #_ #HTU2 #IHU12 #lv #Hlv >(m4 … H1M)
  41   >IHU12 -IHU12 /2 width=1 by li_ldef/
  42   <(sound_fwd_lift … H1M H2M … HTU2) -H2M -HTU2
  43   /2 width=1 by sound_ti_eq_l/
  44 | #G #L #V #T1 #T2 #_ #IHT12 #lv #Hlv >(m7 … H1M) -H1M /2 width=1 by/
  45 | #a #G #L #V1 #V2 #W1 #w2 #T1 #T2 #_ #_ #_ #IHV12 #_ #IHT12 #lv #Hlv
  46   >(m6 … H1M) >(m8 … H1M) >(m4 … H1M) >(m7 … H1M) -H1M
  47   >IHV12 -IHV12 /3 width=1 by li_ldec/
  48 | #a #G #L #V1 #V2 #W2 #U1 #U2 #T1 #T2 #_ #HVW2 #_ #_ #IHV12 #IHU12 #IHT12 #lv #Hlv
  49   >(m6 … H1M) >(m4 … H1M) >(m4 … H1M) >(m6 … H1M)
  50   >IHV12 -IHV12 // <IHU12 -IHU12 // @eq_f2 /3 width=1 by li_ldef/
  51   <(sound_fwd_lift … H1M H2M … HVW2) -H2M -HVW2
  52   /2 width=1 by sound_ti_eq_l/
  53 ]
  54 qed-.