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Definition: function
f is a function : <=> f is a binary relation /\ forall x, y0, y1: (<x, y0> in f /\ <x, y1> in f) => y0=y1.
Definition: partial function from A to B
f: A ->partial B : <=> f is a function /\ f subset A x B.
Definition: (total) function from A to B
f: A -> B : <=> f: A ->partial B /\ forall x in A: exists y in B: <x, y> in f.