matita/matita/contribs/lambdadelta/basic_2/etc_2A1/hod/ntas.etc

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  14
  15 notation "hvbox( ⦃ h , break L ⦄ ⊢ break term 46 T1 : : * break term 46 T2 )"
  16    non associative with precedence 45
  17    for @{ 'NativeTypeStarAlt $h $L $T1 $T2 }.
  18
  19 include "basic_2/dynamic/nta.ma".
  20
  21 (* HIGHER ORDER NATIVE TYPE ASSIGNMENT ON TERMS *****************************)
  22
  23 definition ntas: sh → lenv → relation term ≝
  24                  λh,L. star … (nta h L).
  25
  26 interpretation "higher order native type assignment (term)"
  27    'NativeTypeStar h L T U = (ntas h L T U).
  28
  29 (* Basic eliminators ********************************************************)
  30 (*
  31 lemma cprs_ind: ∀L,T1. ∀R:predicate term. R T1 →
  32                 (∀T,T2. L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → R T → R T2) →
  33                 ∀T2. L ⊢ T1 ➡* T2 → R T2.
  34 #L #T1 #R #HT1 #IHT1 #T2 #HT12
  35 @(TC_star_ind … HT1 IHT1 … HT12) //
  36 qed-.
  37 *)
  38 axiom ntas_ind_dx: ∀h,L,T2. ∀R:predicate term. R T2 →
  39                    (∀T1,T. ⦃h, L⦄ ⊢ T1 : T → ⦃h, L⦄ ⊢ T :* T2 → R T → R T1) →
  40                    ∀T1. ⦃h, L⦄ ⊢ T1 :* T2 → R T1.
  41 (*
  42 #h #L #T2 #R #HT2 #IHT2 #T1 #HT12
  43 @(star_ind_dx … HT2 IHT2 … HT12) //
  44 qed-.
  45 *)
  46 (* Basic properties *********************************************************)
  47
  48 lemma ntas_refl: ∀h,L,T. ⦃h, L⦄ ⊢ T :* T.
  49 // qed.
  50
  51 lemma ntas_strap1: ∀h,L,T1,T,T2.
  52                    ⦃h, L⦄ ⊢ T1 :* T → ⦃h, L⦄  ⊢ T : T2 → ⦃h, L⦄  ⊢ T1 :* T2.
  53 /2 width=3/ qed.
  54
  55 lemma ntas_strap2: ∀h,L,T1,T,T2.
  56                    ⦃h, L⦄  ⊢ T1 : T → ⦃h, L⦄ ⊢ T :* T2 → ⦃h, L⦄ ⊢ T1 :* T2.
  57 /2 width=3/ qed.