# inequality – Can we write \$a leq a\$

I am proving some inequality and one of the steps i took is that i wrote $$n+1 leq n+1$$ is it correct mathematically to write such thing ?

Note :
i was try to prove that $$2^{n-1} leq n! leq n^{n} space space forall n in mathbb{N^*}…P_n$$

so i did it by induction and i got to $$2^{n-1} leq n! leq (n+1)^n$$

then i wrote that $$2 leq n+1 leq n+1$$ and i multiplied the inequalities side by side to get to $$P_{n+1}$$