assumptions – Why a complementary inequality for function values does not simplify to False?


I have a general assumption of a function to be positive. The direct inequality (f(x)>0) does simplify to True, but a complementary one (f(x) < 0) does not simplify at all despite the fact that I explcitly assumed that funciton is not zero.

$Assumptions = K(_) > 0 && K(_) != 0

FullSimplify(K(15) > 0)
True
FullSimplify(K(12) == 0)
False
FullSimplify(K(15) < 0)
K(15) < 0

Thansk in advance,