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// ---------------------------------------------------------------- // $Id: evaluator.tex,v 1.7 1999/09/29 12:28:26 schreine Exp $ // functions // // (c) 1999, Wolfgang Schreiner, see file COPYRIGHT // http://www.risc.uni-linz.ac.at/software/formal // ---------------------------------------------------------------- read relation; // the image of A' at f fun image(f: Function, A': Set) = if(isSubset(A', domain(f)), set(x in A': true, apply(f, x))); // the inverse image of B' at f fun image^-1(f: Function, B': Set) = set(x in domain(f): in(apply(f, x), B'), x); // f is injective from A to B pred isInjective(f: Function, A: Set, B: Set) <=> and(isFunction(f, A, B), forall(x0 in A, x1 in A: implies(=(apply(f, x0), apply(f, x1)), =(x0, x1)))); // f is surjective from A to B pred isSurjective(f: Function, A: Set, B: Set) <=> and(isFunction(f, A, B), forall(y in B: exists(x in A: =(apply(f, x), y)))); // f is bijective between A and B pred isBijective(f: Function, A: Set, B: Set) <=> and(isInjective(f, A, B), isSurjective(f, A, B)); // ---------------------------------------------------------------- // $Id: evaluator.tex,v 1.7 1999/09/29 12:28:26 schreine Exp $ // ----------------------------------------------------------------