$[\![ \forall p \in \dot{G} \,\, \forall q \in \check{\mathcal{A}} \,\, p \leq q \Rightarrow q \in \dot{G} ]\!]=1$.
Notemos que basta mostrar que $[\![ \forall p \in \dot{G} \,\, \forall q \in \check{\mathcal{A}} \,\, p\leq q ]\!] \leq [\![ q \in \dot{G} ]\!]$
Fixemos $a,b \in \mathcal{A}$ quaisquer, assim $[\![ \check{a} \in \dot{G} \,\, \check{b} \in \check{\mathcal{A}} \,\, \check{a}\leq \check{b} ]\!] \leq [\![ \check{b} \in \dot{G} ]\!]$
$[\![ \check{a} \in \dot{G} \,\, \check{b} \in \check{\mathcal{A}} \,\, \check{a}\leq \check{b} ]\!] = [\![\check{a} \in \dot{G} ]\!][\![ \check{b} \in \check{\mathcal{A}}]\!][\![\check{a} \leq \check{b} ]\!] = [\![\check{a} \in \dot{G} ]\!] = a \leq b = [\![\check{b} \in \dot{G} ]\!]$ $\square$