Proof of proveit.linear_algebra.inner_products.ortho_norm_basis_existence_with_any_vector theorem

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

%proving ortho_norm_basis_existence_with_any_vector

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