reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;
reserve L,L0,L1,L2 for Element of line_of_REAL n;

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;
