matita/matita/contribs/lambdadelta/ground/lib/stream.ma

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  14
  15 include "ground/notation/functions/oplusright_3.ma".
  16 include "ground/lib/relations.ma".
  17
  18 (* STREAMS ******************************************************************)
  19
  20 coinductive stream (A:Type[0]): Type[0] ≝
  21 | stream_cons: A → stream A → stream A
  22 .
  23
  24 interpretation
  25   "cons (streams)"
  26   'OPlusRight A a u = (stream_cons A a u).
  27
  28 (* Basic constructions ******************************************************)
  29
  30 lemma stream_rew (A) (t:stream A): match t with [ stream_cons a u ⇒ a ⨮ u ] = t.
  31 #A * //
  32 qed.
  33
  34 (* Basic inversions *********************************************************)
  35
  36 lemma eq_inv_stream_cons_bi (A) (a1,a2:A) (u1) (u2):
  37       a1 ⨮ u1 = a2 ⨮ u2 → ∧∧ a1 = a2 & u1 = u2.
  38 #A #a1 #a2 #u1 #u2 #H destruct
  39 /2 width=1 by conj/
  40 qed-.