matita/matita/contribs/lambda-delta/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: term → Prop ≝
  20    | simple_sort: ∀k. simple (⋆k)
  21    | simple_lref: ∀i. simple (#i)
  22    | simple_flat: ∀I,V,T. simple (𝕗{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] → ∀J,W,U. T = 𝕓{J} W. U → False.
  30 #T * -T
  31 [ #k #J #W #U #H destruct
  32 | #k #J #W #U #H destruct
  33 | #I #V #T #J #W #U #H destruct
  34 ]
  35 qed.
  36
  37 lemma simple_inv_bind: ∀I,V,T. 𝕊[𝕓{I} V. T] → False.
  38 /2 width=6/ qed.