A tropical chart $(V,\varphi_{U})$ on ${X^{\rm an}}$ consists of an open subset $V$ of ${X^{\rm an}}$ contained in ${U^{\rm an}}$ for a very affine open subset $U$ of $X$ with $V={\rm trop}_{U}^{-1}(\Omega)$ for some open subset $\Omega$ of ${\rm Trop}(U)$. Here the canonical moment map $\varphi_{U}:U\rightarrow T_{U}$ from 4.12 plays the role of (tropical) coordinates for $V$. By 4.13, $\varphi_{U}$ is an embedding. The condition $V={\rm trop}_{U}^{-1}(\Omega)$ means that $V$ behaves well with respect to the tropical coordinates. In particular, ${\rm trop}_{U}(V)=\Omega$ is an open subset of ${\rm Trop}(U)$.

We say that the tropical chart $(V^{\prime},\varphi_{U^{\prime}})$ is a tropical subchart of $(V,\varphi_{U})$ if $V^{\prime}\subset V$ and $U^{\prime}\subset U$. We note that the definition of tropical chart here is different from the tropical charts in [CD12], §3.1, which consist of an analytic morphism to a split torus and a finite union of polytopes containing the tropicalization.