Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | Next revision Both sides next revision | ||
sav07_lecture_3 [2007/03/22 13:39] yuanjianwz |
sav07_lecture_3 [2007/03/22 13:43] yuanjianwz |
||
---|---|---|---|
Line 214: | Line 214: | ||
Proof: small model theorem. | Proof: small model theorem. | ||
+ | |||
Line 223: | Line 224: | ||
The idea is to reduce the case, for example: | The idea is to reduce the case, for example: | ||
- | ∃x,y,z.F | + | //∃x,y,z.F// |
reduce to | reduce to | ||
- | ∃x≤ M,y≤ M,z ≤ M.F | + | //∃x≤ M,y≤ M,z ≤ M.F// |
We try to figure out the boundary M. | We try to figure out the boundary M. | ||
Another example: | Another example: | ||
- | ¬t1 < t2 | + | //¬t1 < t2// |
reduce to | reduce to | ||
- | t2+1≤t1 | + | //t2+1≤t1// |
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)// |
First step: transform to disjunctive normal form. | First step: transform to disjunctive normal form. |