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Definition: An inductive definition of a set S is a collection of formulas
where we call the function constants f1, ..., fc the constructors of S.
(forall x1,...,xm1, y1 in S, ..., yn1 in S: f1(x1, ..., xm1, y1, ..., yn1) in S) , ... , (forall x1,...,xmc, y1 in S, ..., ync in S: fc(x1, ..., xmc, y1, ..., ync) in S)