  Multi-indexed orthogonal polynomials describe eigenfunctions of exactly
solvable shape-invariant quantum mechanical systems in one dimension obtained
by the method of virtual states deletion. Multi-indexed orthogonal polynomials
are labeled by a set of degrees of polynomial parts of virtual state
wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi,
Wilson and Askey-Wilson types, two different index sets may give equivalent
multi-indexed orthogonal polynomials. We clarify these equivalences.
Multi-indexed orthogonal polynomials with both type I and II indices are
proportional to those of type I indices only (or type II indices only) with
shifted parameters.
