
theorem Th55:
  for X, A being set, F being Dependency-set of X st A in
charact_set F holds A is Subset of X & ex a, b being Subset of X st [a, b] in F
  & a c= A & not b c= A
proof
  let X, A be set, F be Dependency-set of X;
  assume A in charact_set F;
  then
  ex Y being Subset of X st A = Y & ex a, b being Subset of X st [a, b] in
  F & a c= Y & not b c= Y;
  hence thesis;
end;
