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sav08:partial_congruences [2008/04/23 07:49]
vkuncak
sav08:partial_congruences [2008/04/23 07:50]
vkuncak
Line 15: Line 15:
 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:
 \[ \[
-   \forall x_1,​\ldots,​x_n,​y_1,​\ldots,​y_n. \bigwedge_{i=1}^n (x_i,y_i) \in r \land f(x_1,​\ldots,​x_n) \in T \land f(y_1,​\ldots,​y_n) \in T  \rightarrow (f(x_1,​\ldots,​x_n),​f(y_1,​\ldots,​y_n)) \in r+\begin{array}{l} 
 +   \forall x_1,​\ldots,​x_n,​y_1,​\ldots,​y_n. \bigwedge_{i=1}^n (x_i,y_i) \in r\land f(x_1,​\ldots,​x_n) \in T \land f(y_1,​\ldots,​y_n) \in T  \rightarrow ​\\  
 +    ​(f(x_1,​\ldots,​x_n),​f(y_1,​\ldots,​y_n)) \in r
 \] \]