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Lax314295.KTypesCongruence

k-types are a congruence for concatenation

concepts/Lax314295/KTypesCongruence.lean · lax-314295

proven

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    In the paper

    Theorem

    The kk-type of a concatenation wvwv depends only on the kk-types of ww and of vv (Lemma C.4.15 of Transducers, congruence): the relation "same kk-type" is a congruence of the free monoid.

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    1import Lax314295.KTypes
    2
    3/-!
    4---
    5title: k-types are a congruence for concatenation
    6type: theorem
    7---
    8The kk-type of a concatenation wvwv depends only on the kk-types of ww
    9and of vv (Lemma C.4.15 of *Transducers*, congruence): the relation "same
    10kk-type" is a congruence of the free monoid.
    11
    12# Formalization notes
    13
    14Stated over any alphabet; no finiteness is needed.
    15-/
    16
    17namespace Lax314295.KTypesCongruence
    18
    19open Lax314295.KTypes
    20
    21/-- The `k`-type of a concatenation is determined by the `k`-types of the parts. -/
    22axiom tp_append_congr {A : Type} (k : ℕ) (w w' v v' : List A)
    23 (hw : tp k w = tp k w') (hv : tp k v = tp k v') : tp k (w ++ v) = tp k (w' ++ v')
    24
    25end Lax314295.KTypesCongruence
    26
    Show Proof

    Formalization notes

    Stated over any alphabet; no finiteness is needed.

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