
theorem Th65:
  for C being Coherence_Space, x being set holds x in 'not' C iff
  x c= union C & for a being Element of C ex z being set st x /\ a c= {z}
proof
  let C be Coherence_Space, x be set;
  x in 'not' C iff ex X being Subset of union C st x = X & for a being
  Element of C ex z being set st X /\ a c= {z};
  hence thesis;
end;
