Lax Lean Archive

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

Lax314295.KTypesRefinement

k-types refine each other

concepts/Lax314295/KTypesRefinement.lean · lax-314295

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    Theorem

    Strings with the same (k+1)(k+1)-type have the same kk-type (Lemma C.4.15 of Transducers, refinement): the kk-type of a string is determined by its (k+1)(k+1)-type.

    Lean source view on GitHub

    1import Lax314295.KTypes
    2
    3/-!
    4---
    5title: k-types refine each other
    6type: theorem
    7---
    8Strings with the same (k+1)(k+1)-type have the same kk-type (Lemma C.4.15 of
    9*Transducers*, refinement): the kk-type of a string is determined by its
    10(k+1)(k+1)-type.
    11
    12# Formalization notes
    13
    14Stated over any alphabet; no finiteness is needed.
    15-/
    16
    17namespace Lax314295.KTypesRefinement
    18
    19open Lax314295.KTypes
    20
    21/-- Equal `(k+1)`-types have equal `k`-types. -/
    22axiom tp_eq_of_tp_succ_eq {A : Type} (k : ℕ) (w v : List A) (h : tp (k + 1) w = tp (k + 1) v) :
    23 tp k w = tp k v
    24
    25end Lax314295.KTypesRefinement
    26
    Show Proof

    Formalization notes

    Stated over any alphabet; no finiteness is needed.

    Builds on

    Used by

    none

    From Mathlib

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…