helm/software/matita/contribs/dama/dama/property_exhaustivity.ma

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  14
  15 include "ordered_uniform.ma".
  16
  17 (* Definition 3.7 *)
  18 definition exhaustivity ≝
  19   λC:ordered_uniform_space.
  20    ∀a,b:sequence C.
  21      (a is_increasing → a is_upper_located → a is_cauchy) ∧
  22      (b is_decreasing → b is_lower_located → b is_cauchy).
  23
  24 (* Lemma 3.8 *)