Proof of proveit.physics.quantum.algebra.matrix_simultaneous_diagonalization_as_outer_prods theorem

import proveit
theory = proveit.Theory() # the theorem's theory

%proving matrix_simultaneous_diagonalization_as_outer_prods

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
matrix_simultaneous_diagonalization_as_outer_prods:
(see dependencies)