Lax Lean Archive

While this submission is a draft, it cannot be used by other submissions.

Injective string representations

Lax149335.StringRepresentations · concepts/Lax149335/StringRepresentations.lean · lax-149335

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.

    Natural Language Statement

    Lemma

    Lemma 5.6. For every type AA there is an injective aperiodic term encA:A→2∗\mathsf{enc}_A : A \to 2^*, where 2=1+12 = 1 + 1 is the binary alphabet.

    Concept map
    6 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax149335.InjectiveSurjectiveTerms
    2
    3/-!
    4---
    5title: Injective string representations
    6type: lemma
    7---
    8**Lemma 5.6.** For every type AA there is an injective aperiodic term
    9encA:A→2∗\mathsf{enc}_A : A \to 2^*, where 2=1+12 = 1 + 1 is the binary alphabet.
    10-/
    11
    12namespace Lax149335.StringRepresentations
    13
    14open Lax149335.Types Lax149335.Terms Lax149335.InjectiveSurjectiveTerms
    15
    16/-- **Lemma 5.6.** Every type has an injective aperiodic encoding into binary strings. -/
    17axiom exists_injective_binary_encoding (A : Ty) :
    18 ∃ enc : Term A (Ty.finAlph 1)⋆, IsAperiodic enc ∧ ProvablyInjective enc
    19
    20end Lax149335.StringRepresentations
    21
    Show Proof
    Builds on
    Used by

    none

    From Mathlib

    none

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…