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sav08:partial_congruences [2008/04/23 07:45] vkuncak |
sav08:partial_congruences [2008/04/23 07:49] vkuncak |
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**Proof:** | **Proof:** | ||
- | Show that C^i(s) \cap T^2 = s$ for each $i \ge 0$. | + | Show $C^i(s) \cap T^2 = s$ for all $i \ge 0$. |
**Proof End.** | **Proof End.** | ||
+ | |||
+ | When checking a formula we compute congruences on a finite set of terms that occur in the formula. | ||
+ | |||
+ | We apply the congruence condition only to terms that already exist in the set, using congruence condition: | ||
+ | \[ | ||
+ | \forall x_1,\ldots,x_n,y_1,\ldots,y_n. \bigwedge_{i=1}^n (x_i,y_i) \in r \land f(x_1,\ldots,x_n) \in T \land f(y_1,\ldots,y_n) \in T \rightarrow (f(x_1,\ldots,x_n),f(y_1,\ldots,y_n)) \in r | ||
+ | \] | ||
+ |