Proof of proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult theorem

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

%proving tensor_prod_distribution_over_summation_with_scalar_mult

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