Lax Lean Archive

Integer encodings and distinct 3-SUM entries

Lax489179.EncodingProperties · concepts/Lax489179/EncodingProperties.lean · lax-489179

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

    The signed-integer and optional-integer decoders are left inverses of their encoders. In particular, both encodings are injective. A 3-SUM yes-instance has at least three entries.

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

    This concept declares 5 statements. Each proof establishes one of them relative to its assumptions.

    1 decode_encode_int proven

    2 decode_encode_option proven

    3 encode_int_injective proven

    4 encode_option_injective proven

    5 three_entries proven

    Lean source view on GitHub

    1import Lax489179.IntegerEncoding
    2import Lax489179.ThreeSUM
    3
    4/-!
    5---
    6title: Integer encodings and distinct 3-SUM entries
    7type: lemma
    8---
    9The signed-integer and optional-integer decoders are left inverses of
    10their encoders. In particular, both encodings are injective. A 3-SUM
    11yes-instance has at least three entries.
    12-/
    13
    14namespace Lax489179.EncodingProperties
    15
    16open IntegerEncoding
    17
    18axiom decode_encode_int (z : ℤ) : decodeInt (encodeInt z) = z
    19
    20axiom decode_encode_option (z : Option ℤ) : decodeOption (encodeOption z) = z
    21
    22axiom encode_int_injective : Function.Injective encodeInt
    23
    24axiom encode_option_injective : Function.Injective encodeOption
    25
    26axiom three_entries (input : List ℤ) (h : ThreeSUM.HasZeroSum input) : 3 ≤ input.length
    27
    28end Lax489179.EncodingProperties
    29
    Show ProofShow ProofShow ProofShow ProofShow 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…