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sav08:simple_qe_for_integer_difference_inequalities [2009/04/21 19:17] vkuncak |
sav08:simple_qe_for_integer_difference_inequalities [2009/04/21 19:17] vkuncak |
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| $\forall y \exists x . x \leq y \wedge x \neq y $ | $\forall y \exists x . x \leq y \wedge x \neq y $ | ||
| - | ++|\\ | + | ++++|\\ |
| $\exists x . x \leq y \wedge (x < y \vee y < x)$\\ | $\exists x . x \leq y \wedge (x < y \vee y < x)$\\ | ||
| $\exists x . x \leq y \wedge (x + 1 \leq y \vee y + 1 \leq x)$\\ | $\exists x . x \leq y \wedge (x + 1 \leq y \vee y + 1 \leq x)$\\ | ||
| Line 93: | Line 93: | ||
| Because there are no lower or upper bounds, these formulas are $true$\\ | Because there are no lower or upper bounds, these formulas are $true$\\ | ||
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| + | ++++ | ||
| If we apply this technique to a closed formula in this theory, what formulas do we obtain as a result? | If we apply this technique to a closed formula in this theory, what formulas do we obtain as a result? | ||