A statement-like declaration with \(n \geq 1\) free variables, denoted
\[\begin{equation*}
P(x_1, \ldots, x_n),
\end{equation*}
\]
| where | \(P\) | is the name and |
| \(x_i\) | is the \(i\)-th free variable. |
that becomes a statement when quantified.
Let \(P(x)\) mean “\(x\) is even”. Then
\[\begin{equation*}
\forall x \>\> P(x) \iff \lnot P(x + 1)
\end{equation*}
\]
is a tautology.