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

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  14
  15 include "basic_2/notation/relations/simple_1.ma".
  16 include "basic_2/grammar/term.ma".
  17
  18 (* SIMPLE (NEUTRAL) TERMS ***************************************************)
  19
  20 inductive simple: predicate term ≝
  21    | simple_atom: ∀I. simple (⓪{I})
  22    | simple_flat: ∀I,V,T. simple (ⓕ{I} V. T)
  23 .
  24
  25 interpretation "simple (term)" 'Simple T = (simple T).
  26
  27 (* Basic inversion lemmas ***************************************************)
  28
  29 fact simple_inv_bind_aux: ∀T. 𝐒⦃T⦄ → ∀a,J,W,U. T = ⓑ{a,J} W. U → ⊥.
  30 #T * -T
  31 [ #I #a #J #W #U #H destruct
  32 | #I #V #T #a #J #W #U #H destruct
  33 ]
  34 qed.
  35
  36 lemma simple_inv_bind: ∀a,I,V,T. 𝐒⦃ⓑ{a,I} V. T⦄ → ⊥.
  37 /2 width=7/ qed-.
  38
  39 lemma simple_inv_pair: ∀I,V,T.  𝐒⦃②{I}V.T⦄ → ∃J. I = Flat2 J.
  40 * /2 width=2/ #a #I #V #T #H
  41 elim (simple_inv_bind … H)
  42 qed-.