Proof of `The convergence hypothesis on Lie polynomials` (1st statement)
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The product of factorials divides the total factorial. The multinomial coefficient is one nonnegative summand in the multinomial expansion of the power of the number of variables.