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Boolean-sum symmetry

Lax461425.BooleanSumSymmetry · concepts/Lax461425/BooleanSumSymmetry.lean · lax-461425

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    Natural Language Statement

    Theorem

    Every polynomial of a family in symmetric VNP is invariant under independent row and column permutations of the matrix variables.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
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    1import Lax461425.SymmetricFamilies
    2import Lax461425.SymmetricClasses
    3import Lax461425.SymmetricVNP
    4
    5/-!
    6---
    7title: Boolean-sum symmetry
    8type: theorem
    9---
    10Every polynomial of a family in symmetric VNP is invariant under independent row and
    11column permutations of the matrix variables.
    12-/
    13
    14namespace Lax461425.BooleanSumSymmetry
    15
    16open SymmetricFamilies SymmetricClasses SymmetricVNP
    17
    18/-- Every member of a symmetric VNP family is matrix-invariant. -/
    19axiom matrixInvariant_of_mem {K : Type*} [CommSemiring K] (f : MatrixFamily K)
    20 (hf : InSymVNP f) (n : ℕ) : MatrixInvariant (f n)
    21
    22end Lax461425.BooleanSumSymmetry
    23
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