Draft — mutable and not usable as a dependency; its citation marks the draft state.

Proof of `k-types are aperiodic`

groundedproofs/Lax314295Proofs/Results.lean · lax-314295

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.

Read the Lean proof on GitHub

Description

The kk-types of the powers of a string eventually stabilise (Lemma C.4.15, aperiodicity): an explicit bound tpBoundktpBound k from which on the kk-types of wnwⁿ are constant (Transducers.tppropertiesTransducers.tp_properties, third conjunct).

Proof strategy

Part A's bridge identifies the concept's npownpow with the source's (Lax765601Proofs.Bridge.npoweqLax765601Proofs.Bridge.npow_eq), and tpeqifftp_eq_iff transports the equality of kk-types.

Attribution

Lemma C.4.15 of Transducers, Part C; formalised by Aristotle (Harmonic), PartC/KTypes.leanPartC/KTypes.lean, PartC/MSO.leanPartC/MSO.lean.