refactor: Remove double empty lines
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@ -18,7 +18,6 @@ To define `toSols` we define a series of other maps from various subtypes of
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`MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ` to `MSSMACC.Sols`. And show that these maps form a
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surjection on certain subtypes of `MSSMACC.Sols`.
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# References
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The main reference for the material in this file is:
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@ -78,7 +77,6 @@ lemma linEqPropSol_iff_proj_linEqProp (R : MSSMACC.Sols) :
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rw [h.2.2]
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simp
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/-- A condition which is satisfied if the plane spanned by `R`, `Y₃` and `B₃` lies
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entirely in the quadratic surface. -/
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def InQuadProp (R : MSSMACC.AnomalyFreePerp) : Prop :=
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@ -237,7 +235,6 @@ not surjective. -/
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def toSolNS : MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a, _ , _) =>
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a • AnomalyFreeMk'' (toSolNSQuad R) (toSolNSQuad_cube R)
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/-- A map from `Sols` to `MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ` which on elements of
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`notInLineEqSol` will produce a right inverse to `toSolNS`. -/
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def toSolNSProj (T : MSSMACC.Sols) : MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ :=
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@ -457,7 +454,6 @@ theorem toSol_surjective : Function.Surjective toSol := by
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simp at h₃
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exact toSol_inQuadCube ⟨T, And.intro h₁ (And.intro h₂ h₃)⟩
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end AnomalyFreePerp
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end MSSMACC
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