refactor: Remove double empty lines
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@ -98,7 +98,6 @@ lemma apply_im_smooth (φ : HiggsField) (i : Fin 2):
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/-- Given two `higgsField`, the map `spaceTime → ℂ` obtained by taking their inner product. -/
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def innerProd (φ1 φ2 : HiggsField) : SpaceTime → ℂ := fun x => ⟪φ1 x, φ2 x⟫_ℂ
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/-- Given a `higgsField`, the map `spaceTime → ℝ` obtained by taking the square norm of the
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higgs vector. -/
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@[simp]
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@ -154,7 +153,6 @@ lemma potential_apply (φ : HiggsField) (μSq lambda : ℝ) (x : SpaceTime) :
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simp [HiggsVec.potential, toHiggsVec_norm]
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ring
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/-- A higgs field is constant if it is equal for all `x` `y` in `spaceTime`. -/
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def IsConst (Φ : HiggsField) : Prop := ∀ x y, Φ x = Φ y
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@ -39,7 +39,6 @@ open ComplexConjugate
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/-- The complex vector space in which the Higgs field takes values. -/
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abbrev HiggsVec := EuclideanSpace ℂ (Fin 2)
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/-- The continuous linear map from the vector space `higgsVec` to `(Fin 2 → ℂ)` achieved by
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casting vectors. -/
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def higgsVecToFin2ℂ : HiggsVec →L[ℝ] (Fin 2 → ℂ) where
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@ -144,7 +143,6 @@ lemma potential_snd_term_nonneg (φ : HiggsVec) :
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simp_all only [ge_iff_le, norm_nonneg, pow_nonneg, and_true]
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exact le_of_lt hLam
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lemma zero_le_potential_discrim (φ : HiggsVec) :
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0 ≤ discrim (λ) (- μSq ) (- potential μSq (λ) φ) := by
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have h1 := potential_as_quad μSq (λ) φ
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