For $\theta\in\mathcal{Z}^{1,1}(X)$ we denote by

$${\rm PSH}_{\mathscr{D}}(X,\theta)=\{f\in{\mathscr{D}}(X)\,|\,\theta+c_{1}(\mathcal{O}_{X},{\|\ \|}_{\rm triv}\cdot e^{-f})\in\mathcal{Z}^{1,1}(X)\text{ is semipositive}\}$$

the set of $\theta$-plurisubharmonic ($\theta$-psh for short) model functions. Recall from [GM16, Prop. 3.12] that the set ${\rm PSH}_{\mathscr{D}}(X,\theta)$ is stable under the formation of max.