matita/matita/contribs/lambdadelta/basic_2/etc/ssta/ssta_aaa.etc

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  14
  15 include "basic_2/static/aaa_lift.ma".
  16 include "basic_2/static/ssta.ma".
  17
  18 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
  19
  20 (* Properties on atomic arity assignment for terms **************************)
  21
  22 lemma ssta_aaa: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ → ⦃G, L⦄ ⊢ U ⁝ A.
  23 #h #g #G #L #T #A #H elim H -G -L -T -A
  24 [ #G #L #k #U #l #H
  25   elim (ssta_inv_sort1 … H) -H #_ #H destruct //
  26 | #I #G #L #K #V #B #i #HLK #HV #IHV #U #l #H
  27   elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 [2: #l0 ] #HLK0 #HVW0 #HU [ #H ]
  28   lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H0 destruct
  29   lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
  30   @(aaa_lift … HLK … HU) -HU -L // -HV /2 width=2/
  31 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
  32   elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
  33 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
  34   elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
  35 | #G #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
  36   elim (ssta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3/
  37 | #G #L #V #T #A #_ #_ #IHV #IHT #X #l #H
  38   lapply (ssta_inv_cast1 … H) -H /2 width=2/
  39 ]
  40 qed.