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 Th7:
  x=x1+x2+x3 iff x-x1=x2+x3
proof
  thus x=x1+x2+x3 implies x-x1=x2+x3
  proof
    assume x=x1+x2+x3;
    then x = x1 + (x2 + x3) by RVSUM_1:15;
    hence thesis by Th6;
  end;
  now
    assume x-x1=x2+x3;
    hence x = x1 + (x2 + x3) by Th6
      .= x1 + x2 + x3 by RVSUM_1:15;
  end;
  hence thesis;
end;
