matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc

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  14
  15 include "basic_2/static/ssta_lift.ma".
  16 include "basic_2/unwind/sstas.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma sstas_total_S: ∀h,g,L,l,T,U. ⦃h, L⦄ ⊢ T•[g, l + 1]U →
  23                      ∃∃W. ⦃h, L⦄ ⊢ T •*[g] W & ⦃h, L⦄ ⊢ U •*[g] W.
  24 #h #g #L #l @(nat_ind_plus … l) -l
  25 [ #T #U #HTU
  26   elim (ssta_fwd_correct … HTU) /4 width=4/
  27 | #l #IHl #T #U #HTU
  28   elim (ssta_fwd_correct … HTU) <minus_plus_m_m #V #HUV
  29   elim (IHl … HUV) -IHl -HUV /3 width=4/
  30 ]
  31 qed-.
  32
  33 (* Properties on relocation *************************************************)
  34
  35 lemma sstas_lift: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  36                   ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
  37                   ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •*[g] U2.
  38 #h #g #L1 #T1 #U1 #H @(sstas_ind_alt … H) -T1
  39 [ #T1 #HUT1 #L2 #d #e #HL21 #X #HX #U2 #HU12
  40   >(lift_mono … HX … HU12) -X
  41   elim (lift_total T1 d e) /3 width=10/
  42 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL21 #T2 #HT02 #U2 #HU12
  43   elim (lift_total U0 d e) /3 width=10/
  44 ]
  45 qed.
  46
  47 lemma sstas_inv_lift1: ∀h,g,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 →
  48                        ∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
  49                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 & ⇧[d, e] U1 ≡ U2.
  50 #h #g #L2 #T2 #U2 #H @(sstas_ind_alt … H) -T2
  51 [ #T2 #HUT2 #L1 #d #e #HL21 #U1 #HU12
  52   elim (ssta_inv_lift1 … HUT2 … HL21 … HU12) -HUT2 -HL21 /3 width=3/
  53 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L1 #d #e #HL21 #U1 #HU12
  54   elim (ssta_inv_lift1 … HTU0 … HL21 … HU12) -HTU0 -HU12 #U #HU1 #HU0
  55   elim (IHU01 … HL21 … HU0) -IHU01 -HL21 -U0 /3 width=4/
  56 ]
  57 qed-.