Lax Lean Archive

k-types refine each other

Lax314295.KTypesRefinement · concepts/Lax314295/KTypesRefinement.lean · lax-314295

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    Natural Language Statement

    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.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    In the paper

    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.

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