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Function Applications

Definition: function application

apply(f, x) := such y: <x, y> in f.

Notation: we write f(x) instead of apply(f, x).

Notation: we write f(x0, ..., xn-1) to denote f(<x0, ..., xn-1>).

Proposition: a function maps every argument in its domain to a well-defined result.

forall f: f is function =>
   forall x in domain(f):
      f(x) in range(f) /\  <x, f(x)> in f.

Author: Wolfgang Schreiner
Last Modification: October 14, 1999

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