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sav08:partial_congruences [2008/04/23 07:49] vkuncak |
sav08:partial_congruences [2008/04/23 07:50] vkuncak |
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We apply the congruence condition only to terms that already exist in the set, using congruence condition: | We apply the congruence condition only to terms that already exist in the set, using congruence condition: | ||
\[ | \[ | ||
- | \forall x_1,\ldots,x_n,y_1,\ldots,y_n. \bigwedge_{i=1}^n (x_i,y_i) \in r \land f(x_1,\ldots,x_n) \in T \land f(y_1,\ldots,y_n) \in T \rightarrow (f(x_1,\ldots,x_n),f(y_1,\ldots,y_n)) \in r | + | \begin{array}{l} |
+ | \forall x_1,\ldots,x_n,y_1,\ldots,y_n. \bigwedge_{i=1}^n (x_i,y_i) \in r\ \land \ f(x_1,\ldots,x_n) \in T \land f(y_1,\ldots,y_n) \in T \rightarrow \\ | ||
+ | (f(x_1,\ldots,x_n),f(y_1,\ldots,y_n)) \in r | ||
\] | \] | ||