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predicate_logic [2016/05/01 15:38] nikolaj |
predicate_logic [2016/05/01 15:56] nikolaj |
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I came up with | I came up with | ||
- | $P(!a) \equiv \left(\forall x.\,P(x)\implies x=a\right)$ | + | $\phi(!a) \equiv \phi(a) \land \forall x.\left(\phi(x)\implies x=a\right)$ |
- | for a predicate $P$, expressing that $P$ only holds for the term $a$. | + | for a predicate $P$, expressing that $P$ only holds for the term $a$. Then |
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+ | $\exists! x.\,\phi(x) \equiv \exists x.\,\phi(!x)$ | ||
We also use the abbreviation | We also use the abbreviation |