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| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
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sav08:qe_for_presburger_arithmetic [2008/04/21 21:46] david |
sav08:qe_for_presburger_arithmetic [2008/04/21 21:49] david |
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| Line 94: | Line 94: | ||
| That's it! | That's it! | ||
| + | |||
| Line 112: | Line 113: | ||
| $\exists res, res',i, i'. \neg F$ | $\exists res, res',i, i'. \neg F$ | ||
| - | We can eliminate quantifiers with equalities: $i'= i-1$ | + | We can eliminate quantifiers with equalities: $i'= i-1$ and $res' = res + 2$ |
| $res' + 2i'$ becomes $res' + 2(i-1)$, and $\exists i'$ can be removed | $res' + 2i'$ becomes $res' + 2(i-1)$, and $\exists i'$ can be removed | ||
| Line 119: | Line 120: | ||
| $\exists res, i. \neg (res + 2i = 2x \rightarrow res + 2 + 2(i-1) = 2x)$\\ | $\exists res, i. \neg (res + 2i = 2x \rightarrow res + 2 + 2(i-1) = 2x)$\\ | ||
| - | $\exists res, i. \neg (res + 2i = 2x \rightarrow res + 2i = 2x)$ | + | $\exists res, i. \neg (res + 2i = 2x \rightarrow res + 2i = 2x)$\\ |
| + | $\exists res, i. \neg true$\\ | ||
| + | $false$ | ||
| ===== Some Improvements ===== | ===== Some Improvements ===== | ||