matita/matita/contribs/lambdadelta/basic_2/etc/ssta1/aaa_ssta.etc

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  14
  15 include "basic_2/static/ssta.ma".
  16 include "basic_2/static/aaa_lift.ma".
  17 include "basic_2/static/aaa_da.ma".
  18
  19 (* ATONIC ARITY ASSIGNMENT FOR TERMS ****************************************)
  20
  21 (* Properties on stratified static type assignment for terms ****************)
  22
  23 lemma aaa_ssta_conf: ∀h,g,G,L. Conf3 … (aaa G L) (ssta h g G L).
  24 #h #g #G #L #T #A #H elim H -G -L -T -A
  25 [ #G #L #k #U #H
  26   lapply (ssta_inv_sort1 … H) -H #H destruct //
  27 | #I #G #L #K #V #B #i #HLK #HV #IHV #U #H
  28   elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HU
  29   lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H0 destruct
  30   lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
  31   @(aaa_lift … HLK … HU) -HU -L // -HV /2 width=2/
  32 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
  33   elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
  34 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
  35   elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
  36 | #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
  37   elim (ssta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3/
  38 | #G #L #V #T #A #_ #_ #IHV #IHT #X #H
  39   lapply (ssta_inv_cast1 … H) -H /2 width=2/
  40 ]
  41 qed-.
  42
  43 (* Forward lemmas on stratified static type assignment for terms ************)
  44
  45 lemma aaa_fwd_ssta: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∃U. ⦃G, L⦄ ⊢ T •[h, g] U.
  46 #h #g #G #L #T #A #H elim (aaa_fwd_da … H) -H /2 width=3 by da_ssta/
  47 qed-.