Does Cauchy-Bunyakovsky-Schwarz inequality holds for semi-inner-product space

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Does Cauchy-Bunyakovsky-Schwarz inequality holds for semi-inner-product space, defined in https://en.wikipedia.org/wiki/Semi-inner-product#Semi-inner-products_for_Banach_spaces ?

I have found out in this case, $ <x,y><y,x> \leq <x,x><y,y>$

I have check other posts on MSE but all of them are based on different definition of semi inner product space.

Math newbie thanks you.