theorem
  a in M & b in M & a<>b & M is being_line & c in N & d in N & c <>d & N
  is being_line & a,b // c,d implies M // N
proof
  assume that
A1: a in M & b in M and
A2: a<>b and
A3: M is being_line & c in N & d in N and
A4: c <>d and
A5: N is being_line and
A6: a,b // c,d;
  M = Line(a,b) & N = Line(c,d) by A1,A2,A3,A4,A5,Th54;
  hence thesis by A2,A4,A6;
end;
