theorem Th55:
  (not x in L) & L is being_line implies ex x1,x2 st L = Line(x1,
  x2) & x - x1,x2 - x1 are_lindependent2
proof
  assume ( not x in L)& L is being_line;
  then consider x1,x2 such that
A1: L = Line(x1,x2) & x - x1 _|_ x2 - x1 by Th54;
  take x1;
  take x2;
  thus thesis by A1,Th45;
end;
