matita/matita/contribs/lambdadelta/basic_2/grammar/term_simple.ma

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  14
  15 include "basic_2/grammar/term.ma".
  16
  17 (* SIMPLE (NEUTRAL) TERMS ***************************************************)
  18
  19 inductive simple: predicate term ≝
  20    | simple_atom: ∀I. simple (⓪{I})
  21    | simple_flat: ∀I,V,T. simple (ⓕ{I} V. T)
  22 .
  23
  24 interpretation "simple (term)" 'Simple T = (simple T).
  25
  26 (* Basic inversion lemmas ***************************************************)
  27
  28 fact simple_inv_bind_aux: ∀T. 𝐒⦃T⦄ → ∀a,J,W,U. T = ⓑ{a,J} W. U → ⊥.
  29 #T * -T
  30 [ #I #a #J #W #U #H destruct
  31 | #I #V #T #a #J #W #U #H destruct
  32 ]
  33 qed.
  34
  35 lemma simple_inv_bind: ∀a,I,V,T. 𝐒⦃ⓑ{a,I} V. T⦄ → ⊥.
  36 /2 width=7/ qed-.
  37
  38 lemma simple_inv_pair: ∀I,V,T.  𝐒⦃②{I}V.T⦄ → ∃J. I = Flat2 J.
  39 * /2 width=2/ #a #I #V #T #H
  40 elim (simple_inv_bind … H)
  41 qed-.