I have two types of objects, X and Y, each are recursive structures, and contain different structures sets of tuples containing sets.. etc. The number of elements in X and Y are is the same.
I need to proof that for every x in X, there is a unique y in Y.
Can this be achieved by defining a bijective function which uses recursion to construct a y from each x?
Could I also achieve this proof using a proof by induction, if so how would I lay this out?
Is proof by induction the same a defining a recursive function between two recursive structures?