Proof of `Compositions of flip-flop machines are aperiodic`
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
A composition of flip-flops is aperiodic (the easy half of Theorem A.2.8): a flip-flop satisfies the stabilisation condition, hence the pumping property of Claim A.2.9, and the pumping property is preserved by composition.
Attribution
Theorem A.2.8 of Transducers, right-to-left; Lean proof by Aristotle ().