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Lax489179.EncodingProperties

Integer encodings and distinct 3-SUM entries

concepts/Lax489179/EncodingProperties.lean · lax-489179

proven

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    Concept map

    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.

    1st statement decode_encode_int proven

    2nd statement decode_encode_option proven

    3rd statement encode_int_injective proven

    4th statement encode_option_injective proven

    5th statement three_entries proven

    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.

    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
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