helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma

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  14
  15 include "saturations.ma".
  16 include "o-saturations.ma".
  17 include "relations_to_o-algebra.ma".
  18
  19 (* These are only conversions :-) *)
  20
  21 definition o_operator_of_operator:
  22  ∀C:REL. (Ω \sup C => Ω \sup C) → (POW C ⇒ POW C).
  23  intros (C t);apply t;
  24 qed.
  25
  26 definition is_o_saturation_of_is_saturation:
  27  ∀C:REL.∀R: unary_morphism1 (Ω \sup C) (Ω \sup C).
  28   is_saturation ? R → is_o_saturation ? (o_operator_of_operator ? R).
  29  intros; apply i;
  30 qed.
  31
  32 definition is_o_reduction_of_is_reduction:
  33  ∀C:REL.∀R: unary_morphism1 (Ω \sup C) (Ω \sup C).
  34   is_reduction ? R → is_o_reduction ? (o_operator_of_operator ? R).
  35  intros; apply i;
  36 qed.