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 Th3:
  -a*x = (-a)*x & -a*x = a*(-x)
proof
  thus -a*x = ((-1)*a)*x by EUCLID_4:4
    .= (-a)*x;
  hence -a*x = (a*(-1))*x .= a*(-x) by EUCLID_4:4;
end;
