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The Marriage Theorem, as credited to Philip Hall [7], gives the necessary and sufficient condition allowing us to select a distinct element from each of a finite collection {Ai} of n finite subsets. This selection, called a set of different representatives (SDR), exists if and only if the marriage condition (or Hall condition) is satisfied: The proof which… (More)

We introduce the notion of a permanent [13] of a square matrix. It is a notion somewhat related to a determinant, so we follow closely the approach and theorems already introduced in the Mizar Mathematical Library for the determinant. Unfortunately, the formalization of the latter notion is at its early stage, so we had to prove many very elementary… (More)

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