refactor: Lint
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3 changed files with 13 additions and 10 deletions
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@ -270,11 +270,12 @@ lemma accYY_ext {S T : MSSMCharges.charges}
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rw [hd, hu]
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rfl
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/-- The symmetric bilinear function used to define the quadratic ACC. -/
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@[simps!]
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def quadBiLin : BiLinearSymm MSSMCharges.charges := BiLinearSymm.mk₂ (
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fun S => ∑ i, (Q S.1 i * Q S.2 i + (- 2) * (U S.1 i * U S.2 i) +
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D S.1 i * D S.2 i + (- 1) * (L S.1 i * L S.2 i) + E S.1 i * E S.2 i) +
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(- Hd S.1 * Hd S.2 + Hu S.1 * Hu S.2))
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fun (S, T) => ∑ i, (Q S i * Q T i + (- 2) * (U S i * U T i) +
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D S i * D T i + (- 1) * (L S i * L T i) + E S i * E T i) +
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(- Hd S * Hd T + Hu S * Hu T))
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(by
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intro a S T
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simp only
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@ -146,10 +146,10 @@ def lineQuad (R : MSSMACC.AnomalyFreePerp) (c1 c2 c3 : ℚ) : MSSMACC.QuadSols :
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AnomalyFreeQuadMk' (lineQuadAFL R c1 c2 c3) (lineQuadAFL_quad R c1 c2 c3)
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lemma lineQuad_val (R : MSSMACC.AnomalyFreePerp) (c1 c2 c3 : ℚ) :
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(lineQuad R c1 c2 c3).val = (planeY₃B₃ R
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(c2 * quadBiLin R.val R.val - 2 * c3 * quadBiLin B₃.val R.val)
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(2 * c3 * quadBiLin Y₃.val R.val - c1 * quadBiLin R.val R.val)
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(2 * c1 * quadBiLin B₃.val R.val - 2 * c2 * quadBiLin Y₃.val R.val)).val := by
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(lineQuad R c1 c2 c3).val = (planeY₃B₃ R
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(c2 * quadBiLin R.val R.val - 2 * c3 * quadBiLin B₃.val R.val)
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(2 * c3 * quadBiLin Y₃.val R.val - c1 * quadBiLin R.val R.val)
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(2 * c1 * quadBiLin B₃.val R.val - 2 * c2 * quadBiLin Y₃.val R.val)).val := by
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rfl
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lemma lineQuad_smul (R : MSSMACC.AnomalyFreePerp) (a b c d : ℚ) :
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