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 Th18:
  (x1+x2)-(y1+y2)=(x1-y1)+(x2-y2)
proof
  thus (x1+x2)-(y1+y2) = (x1 + x2) - y1 - y2 by RVSUM_1:39
    .= (x1 + x2) + (-y1+ -y2) by RVSUM_1:15
    .= (x1 - y1) + (x2 - y2) by Th16;
end;
