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sav08:syntax_and_shorthands_of_hol [2008/05/28 01:04] vkuncak |
sav08:syntax_and_shorthands_of_hol [2008/05/28 01:05] vkuncak |
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| \lnot F & (F = false) \\ | \lnot F & (F = false) \\ | ||
| F_1 \land F_2 & (\lambda g.\ g\ true\ true) = (\lambda g.\ F_1\ F_2) \\ | F_1 \land F_2 & (\lambda g.\ g\ true\ true) = (\lambda g.\ F_1\ F_2) \\ | ||
| - | \forall x_{t_1}. F_{t_2} & (\lambda x. F) = (\lambda x. true) \\ | + | \forall x. F & (\lambda x. F) = (\lambda x. true) \\ |
| \end{array} | \end{array} | ||
| \] | \] | ||
| Note that we have defined negation, conjunction, and universal quantification, so all propositional operations and existential quantification are expressible. | Note that we have defined negation, conjunction, and universal quantification, so all propositional operations and existential quantification are expressible. | ||