English gifted mathematician Philip Hall proved a certain theorem regarding matching between members of two distinct sets a.k.a. as Hall’s marriage theorem.

The following statement is a practical example supporting his theorem: If you shuffle a standard deck of 52 cards and then create a row of 13 piles each of 4 cards it will be always possible to pick up a card from each pile to assemble a set of all denominations i.e. 1,2,3…Q,K (different suits, of course).

a. Provide a formal proof.
OR
b. Faute de mieux - a simulation program with 10,000 successful results and no failures will be welcomed.