matita/matita/contribs/lambda_delta/basic_2/dynamic/snv_ssta.ma

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  14
  15 include "basic_2/dynamic/snv.ma".
  16
  17 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
  18
  19 (* Properties on stratified static type assignment for terms ****************)
  20
  21 lemma snv_ssta: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃∃U,l. ⦃h, L⦄ ⊢ T •[g, l] U.
  22 #h #g #L #T #H elim H -L -T
  23 [ #L #k elim (deg_total h g k) /3 width=3/
  24 | * #L #K #V #i #HLK #_ * #W #l0 #HVW
  25   [ elim (lift_total W 0 (i+1)) /3 width=8/
  26   | elim (lift_total V 0 (i+1)) /3 width=8/
  27   ]
  28 | #a #I #L #V #T #_ #_ #_ * /3 width=3/
  29 | #a #L #V #W #W1 #T0 #T1 #l #_ #_ #_ #_ #_ #_ * /3 width=3/
  30 | #L #W #T #U #l #_ #_ #HTU #_ #_ #_ /3 width=3/ (**) (* auto fails without the last #_ *)
  31 ]
  32 qed-.
  33
  34 fact snv_ssta_conf_aux: ∀h,g,L,T. (
  35                            ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] →
  36                            ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 →
  37                            #{L0, T0} < #{L, T} → ⦃h, L0⦄ ⊩ U0 :[g]
  38                         ) →
  39                         ∀L0,T0. ⦃h, L0⦄ ⊩ T0 :[g] →
  40                         ∀U0,l. ⦃h, L0⦄ ⊢ T0 •[g, l + 1] U0 →
  41                         L0 = L → T0 = T → ⦃h, L0⦄ ⊩ U0 :[g].
  42 #h #g #L #T #IH1 #L0 #T0 * -L0 -T0
  43 [
  44 |
  45 |
  46 | #a #L0 #V #W #W0 #T0 #V0 #l0 #HV #HT0 #HVW #HW0 #HTV0 #X #l #H #H1 #H2 destruct
  47   elim (ssta_inv_appl1 … H) -H #U0 #HTU0 #H destruct
  48   lapply (IH1 … HT0 … HTU0 ?) // #HU0
  49   @(snv_appl … HV HU0 HVW HW0) -HV -HU0 -HVW -HW0
  50 | #L0 #W #T0 #W0 #l0 #_ #HT0 #_ #_ #U0 #l #H #H1 #H2 destruct -W0
  51   lapply (ssta_inv_cast1 … H) -H /2 width=5/