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}
Т.о., <tex>\Sigma_{i} \subset \Sigma_{i+1}, \Sigma_{i} \subset \Pi_{i+1} \Rightarrow \Sigma_{i} \subset \Sigma_{i+1} \cap \Pi_{i+1}</tex>.
}}
{{Теорема
|statement = <tex>\Pi_{i} \subset \Sigma_{i+1} \cap \Pi_{i+1}</tex>
|proof = <tex>\left]L \in \Pi_{i} \Rightarrow \exists R : x \in L \Leftrightarrow \forall y_{1} \cdots Q y_{i} : R(x,y_{1},\cdots,y_{i})\right.</tex><br/>
<tex>? L \in \Pi_{i+1} \Leftrightarrow \exists R' : x \in L \Leftrightarrow \forall y_{1} \cdots Q y_{i} \bar{Q} y_{i+1} : R'(x,y_{1},\cdots,y_{i},y_{i+1})</tex>
<br/>
<tex>R'(x,y_{1},\cdots,y_{i+1})</tex> {
return <tex>R(x,y_{1},\cdots,y_{i})</tex>
}
<tex>? L \in \Sigma_{i+1} \Leftrightarrow \exists R'' : x \in L \Leftrightarrow \exists y_{0} \forall y_{1} \cdots Q y_{i} : R''(x,y_{0},y_{1},\cdots,y_{i})</tex>
<br/>
<tex>R''(x,y_{0},y_{1},\cdots,y_{i})</tex> {
return <tex>R(x,y_{1},\cdots,y_{i})</tex>
}
Т.о., <tex>\Pi_{i} \subset \Sigma_{i+1}, \Pi_{i} \subset \Pi_{i+1} \Rightarrow \Pi_{i} \subset \Sigma_{i+1} \cap \Pi_{i+1}</tex>.
}}
