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.

© 2024 Rudolf Adamkovič under GNU General Public License version 3.

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