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Sum Quantifier

Definition: If x is a variable, F is a formula and T is a term, then the following is a term with bound variable x:

(sumx, F T).

The value of this term is 0, if F does not hold for any x; otherwise it is, for every x that satisfies F, the sum of the value of T and of the value of the term for all other x:

(forall x: ~F) => (sumx, F T) = 0;
(forall y: F[x <- y] => (sumx, F T) = T[x <- y] + (sumx, F /\  x != y T)).

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

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