theorem
  for A being non empty set, o,o9 being BinOp of A holds o9 is
  commutative implies (o9 is_right_distributive_wrt o iff o9
  is_left_distributive_wrt o)
proof
  let A be non empty set, o,o9 be BinOp of A;
  assume
A1: o9 is commutative;
  then o9 is_distributive_wrt o iff o9 is_left_distributive_wrt o by Th14;
  hence thesis by A1,Th15;
end;
