matita/matita/contribs/lambdadelta/basic_2/computation/dxprs_lift.ma

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  14
  15 include "basic_2/unfold/sstas_lift.ma".
  16 include "basic_2/computation/cprs_lift.ma".
  17 include "basic_2/computation/dxprs.ma".
  18
  19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  20
  21 (* Relocation properties ****************************************************)
  22
  23 lemma dxprs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K → ∀T1,U1. ⇧[d, e] T1 ≡ U1 →
  24                   ∀h,g,T2. ⦃h, K⦄ ⊢ T1 •*➡*[g] T2 → ∀U2. ⇧[d, e] T2 ≡ U2 →
  25                   ⦃h, L⦄ ⊢ U1 •*➡*[g] U2.
  26 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #T2 * #T
  27 elim (lift_total T d e) /3 width=11/
  28 qed.
  29
  30 lemma dxprs_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
  31                        ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •*➡*[g] U2 →
  32                        ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •*➡*[g] T2.
  33 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * #U #HU1 #HU2
  34 elim (sstas_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HT1 #HTU
  35 elim (cprs_inv_lift1 … HU2 … HLK … HTU) -U -L /3 width=5/
  36 qed-.