Proof of `Hadamard automata and Hadamard-finite series` (5th statement)
What this proof establishes
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 Hadamard-finite series form an effective prevariety over a finite alphabet (paper §5, theorem): the effective prevariety has presentations given by Hadamard automata, and its image is exactly the Hadamard-finite series (by the coincidence, ).