matita/matita/contribs/lambda_delta/basic_2/hod/ntas.ma

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