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Set Sizes

Proposition: If A and B are disjoint with sizes m and n, respectively, then the size of their union is m+n:

forall A, B, m in N, n in N:

(A intersection B = 0 /\  |A| = m /\  |B| = n) => |A union B| = m+n.

The size of the Cartesian product of two sets is the product of their sizes:

forall A, B, m in N, n in N:

(|A| = m /\  |B| = n) => |A x B| = m*n.