refactor: Lint
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46 changed files with 176 additions and 168 deletions
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@ -36,7 +36,7 @@ open minkowskiMetric in
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/-- The Lorentz group is the subset of matrices which preserve the minkowski metric. -/
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def LorentzGroup (d : ℕ) : Set (Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ) :=
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{Λ : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ |
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∀ (x y : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ y⟫ₘ = ⟪x, y⟫ₘ}
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∀ (x y : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ y⟫ₘ = ⟪x, y⟫ₘ}
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namespace LorentzGroup
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/-- Notation for the Lorentz group. -/
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@ -145,7 +145,7 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
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smul_eq_mul, LinearMap.neg_apply]
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field_simp
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rw [u.1.2, v.1.2, minkowskiMetric.symm v.1.1 u, minkowskiMetric.symm u y,
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minkowskiMetric.symm v y]
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minkowskiMetric.symm v y]
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ring
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/-- A generalised boost as an element of the Lorentz Group. -/
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@ -63,7 +63,7 @@ lemma not_orthochronous_iff_le_zero :
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/-- The continuous map taking a Lorentz transformation to its `0 0` element. -/
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def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => timeComp Λ,
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Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
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Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
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/-- An auxillary function used in the definition of `orthchroMapReal`. -/
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def stepFunction : ℝ → ℝ := fun t =>
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@ -72,7 +72,7 @@ def stepFunction : ℝ → ℝ := fun t =>
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lemma stepFunction_continuous : Continuous stepFunction := by
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apply Continuous.if ?_ continuous_const (Continuous.if ?_ continuous_const continuous_id)
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<;> intro a ha
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<;> intro a ha
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rw [@Set.Iic_def, @frontier_Iic, @Set.mem_singleton_iff] at ha
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rw [ha]
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simp [neg_lt_self_iff, zero_lt_one, ↓reduceIte]
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@ -157,7 +157,7 @@ def orthchroRep : LorentzGroup d →* ℤ₂ where
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map_mul' Λ Λ' := by
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simp only
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by_cases h : IsOrthochronous Λ
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<;> by_cases h' : IsOrthochronous Λ'
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<;> by_cases h' : IsOrthochronous Λ'
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rw [orthchroMap_IsOrthochronous h, orthchroMap_IsOrthochronous h',
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orthchroMap_IsOrthochronous (mul_othchron_of_othchron_othchron h h')]
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rfl
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