matita/matita/contribs/lambdadelta/basic_2/etc/xpr/xprs_lift.etc

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  14
  15 include "basic_2/reducibility/xpr_lift.ma".
  16 include "basic_2/computation/cprs.ma".
  17 include "basic_2/computation/xprs.ma".
  18
  19 (* EXTENDED PARALLEL COMPUTATION ON TERMS ***********************************)
  20
  21 (* Advanced forward lemmas **************************************************)
  22
  23 lemma xprs_fwd_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1. T1 •➡*[g] U2 →
  24                       ∃∃V2,T2. L ⊢ V1 ➡* V2 & U2 = ⓛ{a}V2. T2.
  25 #h #g #a #L #V1 #T1 #U2 #H @(xprs_ind … H) -U2 /2 width=4/
  26 #U #U2 #_ #HU2 * #V #T #HV1 #H destruct
  27 elim (xpr_inv_abst1 … HU2) -HU2 #V2 #T2 #HV2 #_ #H destruct /3 width=4/
  28 qed-.
  29
  30 (* Relocation properties ****************************************************)
  31
  32 lemma xprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
  33                  ∀h,g,T2. ⦃h, K⦄ ⊢ T1 •➡*[g] T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
  34                  ⦃h, L⦄ ⊢ U1 •➡*[g] U2.
  35 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #T2 #HT12 @(xprs_ind … HT12) -T2
  36 [ -HLK #T2 #HT12
  37    <(lift_mono … HTU1 … HT12) -T1 //
  38 | -HTU1 #T #T2 #_ #HT2 #IHT2 #U2 #HTU2
  39   elim (lift_total T d e) #U #HTU
  40   lapply (xpr_lift … HLK … HTU … HTU2 … HT2) -T2 -HLK /3 width=3/
  41 ]
  42 qed.
  43
  44 lemma xprs_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
  45                       ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •➡*[g] U2 →
  46                       ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •➡*[g] T2.
  47 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 #HU12 @(xprs_ind … HU12) -U2 /2 width=3/
  48 -HTU1 #U #U2 #_ #HU2 * #T #HTU #HT1
  49 elim (xpr_inv_lift1 … HLK … HTU … HU2) -U -HLK /3 width=5/
  50 qed.