theorem Th18:
  A is being_line implies ex a,b st a in A & b in A & a<>b
proof
  assume A is being_line;
  then consider a,b such that
A1: a<>b and
A2: A=Line(a,b);
A3: b in A by A2,Th14;
  a in A by A2,Th14;
  hence thesis by A1,A3;
end;
