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

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  14
  15 include "basic_2/static/ssta_lift.ma".
  16 include "basic_2/reducibility/cpr_lift.ma".
  17 include "basic_2/reducibility/xpr.ma".
  18
  19 (* EXTENDED PARALLEL REDUCTION ON TERMS *************************************)
  20
  21 (* Advanced inversion lemmas ************************************************)
  22
  23 lemma xpr_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1.T1 •➡[g] U2 →
  24                      ∃∃V2,T2. L ⊢ V1 ➡ V2 & ⦃h, L. ⓛV1⦄ ⊢ T1 •➡[g] T2 &
  25                               U2 = ⓛ{a}V2. T2.
  26 #h #g #a #L #V1 #T1 #U2 *
  27 [ #H elim (cpr_inv_abst1 … H Abst V1) /3 width=5/
  28 | #l #H elim (ssta_inv_bind1 … H) /3 width=5/
  29 ]
  30 qed-.
  31
  32 (* Relocation properties ****************************************************)
  33
  34 lemma xpr_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
  35                 ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 →
  36                 ∀h,g. ⦃h, K⦄ ⊢ T1 •➡[g] T2 → ⦃h, L⦄ ⊢ U1 •➡[g] U2.
  37 #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #h #g *
  38 /3 width=9/ /3 width=10/
  39 qed.
  40
  41 lemma xpr_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
  42                      ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •➡[g] U2 →
  43                      ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •➡[g] T2.
  44 #L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * [ #HU12 | #l #HU12 ]
  45 [ elim (cpr_inv_lift1 … HLK … HTU1 … HU12) -L -U1 /3 width=3/
  46 | elim (ssta_inv_lift1 … HU12 … HLK … HTU1) -L -U1 /3 width=4/
  47 ]
  48 qed-.