Let $L$ be a line bundle on the boundaryless paracompact strictly $K$-analytic space $V$ and let ${\|\hskip 4.30554pt\|}$ be a formal metric on $L$. Then ${\|\hskip 4.30554pt\|}$ is a semipositive formal metric as globally defined in 3.2 if and only if ${\|\hskip 4.30554pt\|}$ is a semipositive piecewise linear metric in every $x\in V$ as defined in 3.7.