matita/matita/contribs/lambdadelta/basic_2/etc_2A1/nta/nta_sta.etc

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  14
  15 include "basic_2/static/sta.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17 include "basic_2/dynamic/nta.ma".
  18
  19 (* NATIVE TYPE ASSIGNMENT ON TERMS ******************************************)
  20
  21 (* Properties on static type assignment *************************************)
  22
  23 lemma nta_fwd_sta: ∀h,L,T,U. ⦃h, L⦄ ⊢ T : U →
  24                    ∃∃U0. ⦃h, L⦄ ⊢ T • U0 & L ⊢ U0 ⬌* U.
  25 #h #L #T #U #H elim H -L -T -U
  26 [ /2 width=3/
  27 | #L #K #V #W1 #V1 #i #HLK #_ #HWV1 * #W0 #HVW0 #HW01
  28   elim (lift_total W0 0 (i+1)) #V0 #HWV0
  29   lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
  30   lapply (cpcs_lift … HLK0 … HWV0 … HWV1 HW01) -HLK0 -HWV1 -HW01 /3 width=6/
  31 | #L #K #W #V1 #W1 #i #HLK #HWV1 #HW1 * /3 width=6/
  32 | #I #L #V #W #T #U #_ #_ * #W0 #_ #_ * /3 width=3/
  33 | #L #V #W #T #U #_ #_ * #W0 #_ #HW0 * #X #H #HX
  34   elim (sta_inv_bind1 … H) -H #U0 #HTU0 #H destruct
  35   @(ex2_1_intro … (ⓐV.ⓛW.U0)) /2 width=1/ /3 width=1/
  36 | #L #V #W #T #U #_ #_ * #U0 #HTU0 #HU0 #_ -W
  37   @(ex2_1_intro … (ⓐV.U0)) /2 width=1/
  38 | #L #T #U #HTU * #U0 #HTU0 #HU0 /3 width=3/
  39 | #L #T #U1 #U2 #V2 #_ #HU12 #_ * #U0 #HTU0 #HU01 #_
  40   lapply (cpcs_trans … HU01 … HU12) -U1 /2 width=3/
  41 ]
  42 qed-.