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
  (x1+x2+x3)-(y1+y2+y3)=(x1-y1)+(x2-y2)+(x3-y3)
proof
  thus (x1+x2+x3)-(y1+y2+y3) = ((x1+x2) - (y1+y2))+ (x3 - y3) by Th18
    .= (x1 - y1) + (x2 - y2) + (x3 - y3) by Th18;
end;
