  An operator set is functionally incomplete if it can not represent the full
set $\lbrace \neg,\vee,\wedge,\rightarrow,\leftrightarrow\rbrace$. The
verification for the functional incompleteness highly relies on constructive
proofs. The judgement with a large untested operator set can be inefficient.
Given with a mass of potential operators proposed in various logic systems, a
general verification method for their functional completeness is demanded. This
paper offers an universal verification for the functional completeness.
Firstly, we propose two abstract operators $\widehat{R}$ and $\breve{R}$, both
of which have no fixed form and are only defined by several weak constraints.
Specially, $\widehat{R}_{\geq}$ and $\breve{R}_{\geq}$ are the abstract
operators defined with the total order relation $\geq$. Then, we prove that any
operator set $\mathfrak{R}$ is functionally complete if and only if it can
represent the composite operator $\widehat{R}_{\geq}\circ\breve{R}_{\geq}$ or
$\breve{R}_{\geq}\circ\widehat{R}_{\geq}$. Otherwise $\mathfrak{R}$ is
determined to be functionally incomplete. This theory can be generally applied
to any untested operator set to determine whether it is functionally complete.
