matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_nta.ma

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  14
  15 include "basic_2/dynamic/nta.ma".
  16 include "basic_2/i_dynamic/ntas.ma".
  17
  18 (* ITERATED NATIVE TYPE ASSIGNMENT FOR TERMS ********************************)
  19
  20 (*
  21
  22 definition ntas: sh → lenv → relation term ≝
  23                  λh,L. star … (nta h L).
  24
  25 (* Basic eliminators ********************************************************)
  26
  27 axiom ntas_ind_dx: ∀h,L,T2. ∀R:predicate term. R T2 →
  28                    (∀T1,T. ⦃h,L⦄ ⊢ T1 : T → ⦃h,L⦄ ⊢ T :* T2 → R T → R T1) →
  29                    ∀T1. ⦃h,L⦄ ⊢ T1 :* T2 → R T1.
  30 (*
  31 #h #L #T2 #R #HT2 #IHT2 #T1 #HT12
  32 @(star_ind_dx … HT2 IHT2 … HT12) //
  33 qed-.
  34 *)
  35 (* Basic properties *********************************************************)
  36
  37 lemma ntas_strap1: ∀h,L,T1,T,T2.
  38                    ⦃h,L⦄ ⊢ T1 :* T → ⦃h,L⦄  ⊢ T : T2 → ⦃h,L⦄  ⊢ T1 :* T2.
  39 /2 width=3/ qed.
  40
  41 lemma ntas_strap2: ∀h,L,T1,T,T2.
  42                    ⦃h,L⦄  ⊢ T1 : T → ⦃h,L⦄ ⊢ T :* T2 → ⦃h,L⦄ ⊢ T1 :* T2.
  43 /2 width=3/ qed.
  44 *)