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 Th8:
  -(x1 + x2 + x3) = -x1 + -x2 + -x3
proof
  thus -(x1+x2+x3) = 0*n -(x1+x2+x3) by RVSUM_1:33
    .= 0*n - (x1+x2) - x3 by RVSUM_1:39
    .= 0*n - x1 - x2 - x3 by RVSUM_1:39
    .= -x1 + -x2 + -x3 by RVSUM_1:33;
end;
