$\forall$${\it ea}$,${\it eb}$:($\mathbb{N}$ List), $x$:(?$\mathbb{B}$), $f$,$g$:($\mathbb{N}\rightarrow\mathbb{B}$). combine{-}halt{-}info(${\it ea}$; ${\it eb}$; $f$; $g$; $x$) $\in$ (?$\mathbb{B}$)