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auto-task(PlaneSeven.B): remove B₀–B₆ definitions in favour of a single B : Fin 7 → Charges#1349

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auto-task(PlaneSeven.B): remove B₀–B₆ definitions in favour of a single B : Fin 7 → Charges#1349
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Summary

Completes the TODO in
Physlib/Particles/BeyondTheStandardModel/RHN/AnomalyCancellation/Ordinary/DimSevenPlane.lean:

Remove the definitions of elements (SM 3).Charges B₀, B₁ etc, here [use] only
B : Fin 7 → (SM 3).Charges.

The seven separate top-level definitions B₀, B₁, …, B₆ are removed. The basis of the
dimension-7 plane is now provided solely by the single function
B : Fin 7 → (SM 3).Charges, defined directly by inlining each basis element as an arm
of its match. The helper lemmas (Bᵢ_cubic, Bᵢ_Bi_cubic) and
basis_linear_independent are restated/adjusted to refer to B 0, …, B 6 instead of the
removed Bᵢ; the underlying proof tactics are unchanged apart from unfolding B in place
of the individual definitions. The TODO marker is deleted.

No change to statements or proofs of the public results B_in_accCube, B_sum_is_sol,
basis_linear_independent, or seven_dim_plane_exists.

How to review

  • Confirm the seven def B₀ … def B₆ are gone and the file defines a single
    abbrev B : Fin 7 → (SM 3).Charges (grep: grep -nE 'def B[₀-₆]|abbrev B' <file>
    shows only the abbrev B line).
  • Confirm the TODO "..." note is removed.
  • lake build Physlib.Particles.BeyondTheStandardModel.RHN.AnomalyCancellation.Ordinary.DimSevenPlane
    succeeds with no errors and no warnings.
  • No sorry, and #print axioms SMRHN.SM.seven_dim_plane_exists reports only
    propext, Classical.choice, Quot.sound (no new axioms).

…le B : Fin 7 → Charges

Co-authored-by: Claude <noreply@anthropic.com>
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github-actions Bot commented Jul 1, 2026

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Thank you for this PR, which will now be reviewed. If submitting to ./Physlib or ./QuantumInfo, please see our review guidelines if you are not familiar with the process. You should expect a back and forth with a reviewer before your PR is merged. See also that link for how to add appropriate labels to your PR. The PR will also go through a number of automated checks. You can learn more about these here, including how to run them locally.

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