1. $A$ : Type
\\[0ex]2. $P$ : $A$$\rightarrow\mathbb{N}\rightarrow\mathbb{B}$
\\[0ex]3. $\forall$$x$:$A$. Dec($\exists$$n$:$\mathbb{N}$. ($\uparrow$($P$($x$,$n$))))
\\[0ex]$\vdash$  TERMOF\{p{-}mu{-}decider:ObjectId, 1:l, 1:l\} $\sim$ TERMOF\{p{-}mu{-}decider:ObjectId, 1:l, i:l\}