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9 lines
576 B
9 lines
576 B
The axioms $\mathcal{A}_{EUF}$ are the following:
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\begin{enumerate}
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\item $\forall x.~~x = x$ (reflexivity)
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\item $\forall x, y.~~x = y \rightarrow y = x$ (symmetry)
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\item $\forall x, y, z.~~x = y \wedge y = z \rightarrow x = z$ (transitivity)
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\item $\forall \overline{x}, \overline{y}.~~ ( \bigwedge_{i=1}^n x_i = y_i ) \rightarrow f(\overline{x}) = f(\overline{y})$ (congruence)
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\item $\forall \overline{x}, \overline{y}.~~ ( \bigwedge_{i=1}^n x_i = y_i ) \rightarrow (P(\overline{x}) \leftrightarrow P(\overline{y}))$ (equivalence)
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\end{enumerate}
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