matita/matita/contribs/lambdadelta/ground/etc/relocation/trace_isun.etc

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  14
  15 include "ground_2/notation/relations/isuniform_1.ma".
  16 include "ground_2/relocation/trace_isid.ma".
  17
  18 (* RELOCATION TRACE *********************************************************)
  19
  20 inductive isun: predicate trace ≝
  21 | isun_id   : ∀t. 𝐈⦃t⦄ → isun t
  22 | isun_false: ∀t. isun t → isun (Ⓕ@t)
  23 .
  24
  25 interpretation "test for uniformity (trace)"
  26    'IsUniform t = (isun t).
  27
  28 (* Basic inversion lennas ***************************************************)
  29
  30 fact isun_inv_true_aux: ∀t. 𝐔⦃t⦄ → ∀u. t = Ⓣ@u → 𝐈⦃u⦄.
  31 #t * -t
  32 [ #t #Ht #u #H destruct /2 width=1 by isid_inv_true/
  33 | #t #_ #u #H destruct
  34 ]
  35 qed-.
  36
  37 lemma isun_inv_true: ∀t. 𝐔⦃Ⓣ@t⦄ → 𝐈⦃t⦄.
  38 /2 width=3 by isun_inv_true_aux/ qed-.
  39
  40 fact isun_inv_false_aux: ∀t. 𝐔⦃t⦄ → ∀u. t = Ⓕ@u → 𝐔⦃u⦄.
  41 #t * -t
  42 [ #t #Ht #u #H destruct elim (isid_inv_false … Ht)
  43 | #t #Ht #u #H destruct //
  44 ]
  45 qed-.
  46
  47 lemma isun_inv_false: ∀t. 𝐔⦃Ⓕ@t⦄ → 𝐔⦃t⦄.
  48 /2 width=3 by isun_inv_false_aux/ qed-.