Is this a valid conclusion?

If I have 4 variables, X(0),X(1),X(2) and X(3)

And y1 <= X(i) <= z1

And y2 <= X(0)+X(1) <= z2
And y2 <= X(2)+X(3) <= z2

And y3 <= X(0)+X(3) <= z3
And y3 <= X(1)+X(2) <= z3

And y4 <= X(0)+X(2) <= z4
And y4 <= X(1)+X(3) <= z4

And also,
The limits of every combination of these 4 variables taken 3 at a time are identical { y5 <= [X(0)+X(1)+X(2)], [X(0)+X(1)+X(3)]... }

Can I conclude that y2=y3=y4 and z2=z3=z4?


[edit]
It seems so:

Since x(0) + [x(1) + x(2)] = [x(0) + x(1)] + x(2)
and because the limits of x(0) and the limits of x(2) are identical,
then the limits of [x(1)+x(2)] must be identical to the limits of [x(0)+x(1)]
Which makes y3=y2 and z3=z2.