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

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/dynamic/nta_lift.ma".
  16
  17 (* NATIVE TYPE ASSIGNMENT ON TERMS ******************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 (* Basic_1: was: ty3_unique *)
  22 theorem nta_mono: ∀h,L,T,U1. ⦃h, L⦄ ⊢ T : U1 → ∀U2. ⦃h, L⦄ ⊢ T : U2 →
  23                   L ⊢ U1 ⬌* U2.
  24 #h #L #T #U1 #H elim H -L -T -U1
  25 [ #L #k #X #H
  26   lapply (nta_inv_sort1 … H) -H //
  27 | #L #K #V #W11 #W12 #i #HLK #_ #HW112 #IHVW11 #X #H
  28   elim (nta_inv_lref1 … H) -H * #K0 #V0 #W21 #W22 #HLK0 #HVW21 #HW212 #HX
  29   lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct
  30   lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
  31   @(cpcs_trans … HX) -X /3 width=9 by cpcs_lift/ (**) (* to slow without trace *)
  32 | #L #K #W #V1 #V #i #HLK #_ #HWV #_ #X #H
  33   elim (nta_inv_lref1 … H) -H * #K0 #W0 #V2 #V0 #HLK0 #_ #HWV0 #HX
  34   lapply (ldrop_mono … HLK0 … HLK) -HLK0 -HLK #H destruct
  35   lapply (lift_mono … HWV0 … HWV) -HWV0 -HWV #H destruct //
  36 | #I #L #V #W1 #T #U1 #_ #_ #_ #IHTU1 #X #H
  37   elim (nta_inv_bind1 … H) -H #W2 #U2 #_ #HTU2 #H
  38   @(cpcs_trans … H) -X /3 width=1/
  39 | #L #V #W1 #T #U1 #_ #_ #_ #IHTU1 #X #H
  40   elim (nta_fwd_pure1 … H) -H #U2 #W2 #_ #HTU2 #H
  41   @(cpcs_trans … H) -X /3 width=1/
  42 | #L #V #W1 #T #U1 #_ #_ #IHTU1 #_ #X #H
  43   elim (nta_fwd_pure1 … H) -H #U2 #W2 #_ #HTU2 #H
  44   @(cpcs_trans … H) -X /3 width=1/
  45 | #L #T #U1 #_ #_ #X #H
  46   elim (nta_inv_cast1 … H) -H //
  47 | #L #T #U11 #U12 #V12 #_ #HU112 #_ #IHTU11 #_ #U2 #HTU2
  48   @(cpcs_canc_sn … HU112) -U12 /2 width=1/
  49 ]
  50 qed-.
  51
  52 (* Advanced properties ******************************************************)
  53
  54 lemma nta_cast_alt: ∀h,L,T,W,U. ⦃h, L⦄ ⊢ T : W → ⦃h, L⦄ ⊢ T : U →
  55              ⦃h, L⦄ ⊢ ⓝW.T : U.
  56 #h #L #T #W #U #HTW #HTU
  57 lapply (nta_mono … HTW … HTU) #HWU
  58 elim (nta_fwd_correct … HTU) -HTU /3 width=3/
  59 qed.