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sav07_lecture_3 [2007/03/22 13:35] yuanjianwz |
sav07_lecture_3 [2007/03/22 13:36] yuanjianwz |
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| Proof: small model theorem. | Proof: small model theorem. | ||
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| Line 224: | Line 225: | ||
| ∃x≤ M,y≤ M,z ≤ M.F | ∃x≤ M,y≤ M,z ≤ M.F | ||
| We try to figure out M. | We try to figure out M. | ||
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| Another example: | Another example: | ||
| ¬t1 < t2 | ¬t1 < t2 | ||
| reduce to | reduce to | ||
| t2+1≤t1 | t2+1≤t1 | ||
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| How about the not equal ? | How about the not equal ? | ||
| t1≠t2 | t1≠t2 | ||
| can be reduced to | can be reduced to | ||
| (t1 < t2 ) ∨ (t2 < t1) => (t1 ≤ t2-1) ∨ (t2 ≤ t1-1) | (t1 < t2 ) ∨ (t2 < t1) => (t1 ≤ t2-1) ∨ (t2 ≤ t1-1) | ||
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| First step: transform to disjunctive normal form. | First step: transform to disjunctive normal form. | ||