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Proposition: If A and B have size m and n, respectively, then the size of the set of functions from A to B is nm:
forall A, B, m in N, n in N: (|A| = m /\ |B| = n) => |A -> B| = nm.
If A is of size n, then A has 2n subsets:
forall A, n in N: |A| = n => |P(A)| = 2n.