matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_lift.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/static/ssta_lift.ma".
  16 include "basic_2/unwind/sstas.ma".
  17
  18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma ssta_sstas: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l+1] U → ⦃h, L⦄ ⊢ T •*[g] U.
  23 #h #g #L #T #U #l #HTU
  24 elim (ssta_fwd_correct … HTU) /3 width=4/
  25 qed.
  26
  27 (* Properties on relocation *************************************************)
  28
  29 lemma sstas_lift: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
  30                   ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
  31                   ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •*[g] U2.
  32 #h #g #L1 #T1 #U1 #H @(sstas_ind_alt … H) -T1
  33 [ #T1 #l #HUT1 #L2 #d #e #HL21 #X #HX #U2 #HU12
  34   >(lift_mono … HX … HU12) -X
  35   elim (lift_total T1 d e) /3 width=11/
  36 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL21 #T2 #HT02 #U2 #HU12
  37   elim (lift_total U0 d e) /3 width=10/
  38 ]
  39 qed.
  40
  41 (* Inversion lemmas on relocation *******************************************)
  42
  43 lemma sstas_inv_lift1: ∀h,g,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 →
  44                        ∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
  45                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 & ⇧[d, e] U1 ≡ U2.
  46 #h #g #L2 #T2 #U2 #H @(sstas_ind_alt … H) -T2
  47 [ #T2 #l #HUT2 #L1 #d #e #HL21 #U1 #HU12
  48   elim (ssta_inv_lift1 … HUT2 … HL21 … HU12) -HUT2 -HL21 /3 width=3/
  49 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L1 #d #e #HL21 #U1 #HU12
  50   elim (ssta_inv_lift1 … HTU0 … HL21 … HU12) -HTU0 -HU12 #U #HU1 #HU0
  51   elim (IHU01 … HL21 … HU0) -IHU01 -HL21 -U0 /3 width=4/
  52 ]
  53 qed-.