theorem Th27:
  a,b // A implies ex c,d st c <>d & c in A & d in A & a,b // c,d
  proof
    assume a,b // A;
    then consider c,d such that
A1: c <>d and
A2: A=Line(c,d) and
A3: a,b // c,d;
A4: d in A by A2,Th14;
    c in A by A2,Th14;
    hence thesis by A1,A3,A4;
  end;
