reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem Th9: :: AFF_1:26
  x1 in Line(x1,x2) & x2 in Line(x1,x2)
proof
A1: 1 - 0 = 1 & 1*x1 = x1 by Th3;
A2: 1 - 1 = 0 & (0)*x1 = 0*n by Th3;
A3: 1*x2 = x2 & 0*n + x2 = x2 by Th1,Th3;
  (0)*x2 = 0*n & x1 + 0*n = x1 by Th1,Th3;
  hence thesis by A1,A2,A3;
end;
