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 Th65:
  L1 is being_line & L1 = L2 implies L1 // L2
proof
  assume L1 is being_line;
  then consider x0,x1 such that
A1: x0 <> x1 and
A2: L1 = Line(x0,x1);
  assume
A3: L1 = L2;
A4: x1 - x0 = 1 * (x1 - x0) by EUCLID_4:3;
  x1 - x0 <> 0*n by A1,Th9;
  then x1 - x0 // x1 - x0 by A4;
  hence thesis by A3,A2;
end;
