Questionnaire-2024/smt/0006_sol.tex

The axioms $\mathcal{A}_{EUF}$ are the following:

\begin{enumerate}
    \item  $\forall x.~~x = x$ (reflexivity)
    \item  $\forall x, y.~~x = y \rightarrow y = x$ (symmetry)
    \item  $\forall x, y, z.~~x = y \wedge y = z \rightarrow x = z$ (transitivity)
    \item  $\forall \overline{x}, \overline{y}.~~ ( \bigwedge_{i=1}^n x_i = y_i ) \rightarrow f(\overline{x}) = f(\overline{y})$ (congruence)
    \item  $\forall \overline{x}, \overline{y}.~~ ( \bigwedge_{i=1}^n x_i = y_i ) \rightarrow (P(\overline{x}) \leftrightarrow P(\overline{y}))$ (equivalence)
\end{enumerate}