<s>[INST] Proving $x^2 - y^2 + z^2 \gt (x - y + z)^2$ Prove that

$$x^2 - y^2 + z^2 > (x - y + z)^2$$

where: $x < y <z$  for all natural numbers.
Thank for help.
 [/INST] Hints:
$(x-y+z)^2-z^2=(x-y)(x-y+2z) > (x-y)(x-y+2y)=(x-y)(x+y)\\=x^2-y^2$
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