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 Th6:
  x1 = x2 + x3 iff x2 = x1 - x3
proof
  thus x1 = x2 + x3 implies x2 = x1 - x3
  proof
    assume x1 = x2 + x3;
    hence x1 - x3 = x2 + (x3 + -x3) by RVSUM_1:15
      .= x2 + 0*n by Th2
      .= x2 by EUCLID_4:1;
  end;
  now
    assume x2 = x1 - x3;
    hence x2 + x3 = x1 + (-x3 + x3) by RVSUM_1:15
      .= x1 + 0*n by Th2
      .= x1 by EUCLID_4:1;
  end;
  hence thesis;
end;
