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;

theorem Th14:
  x - (a1*x1+a2*x2+a3*x3) = x + ((-a1)*x1 + (-a2)*x2 + (-a3)*x3)
proof
  thus x - (a1*x1+a2*x2+a3*x3) = x + (-a1*x1 + -a2*x2 + -a3*x3) by Th8
    .= x + ((-a1)*x1 + -a2*x2 + -a3*x3) by Th3
    .= x + ((-a1)*x1 + (-a2)*x2 + -a3*x3) by Th3
    .= x + ((-a1)*x1 + (-a2)*x2 + (-a3)*x3) by Th3;
end;
