Proof of `The correctly annotated strings of an MSO relabelling form a regular language`
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.
In the paper
- page 122 of the paper of lax-157538, Transducers
Description
For an mso relabelling, the strings annotated at every position with a formula true there form a regular language (Claim C.4.6): the intersection, over the formulas, of the complements of the languages "some position carries a formula that fails there", each regular by Lemma C.4.2 ().
Proof strategy
The concept's relabelling is sent to , whose index type is and whose formulas are ; the two languages are equal by extensionality and .
Attribution
Claim C.4.6 of Transducers, Part C; formalised by Aristotle (Harmonic), , .