theorem Th19:
  A is being_line implies ex b st a<>b & b in A
proof
  assume A is being_line;
  then consider p,q such that
A1: p in A and
A2: q in A and
A3: p<>q by Th18;
  a=p implies a<>q & q in A by A2,A3;
  hence thesis by A1;
end;
