refactor: pass at removing double spaces
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jstoobysmith
parent
1fe51b2e04
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1133b883f3
19 changed files with 121 additions and 121 deletions
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@ -40,19 +40,19 @@ def S₂₃ (V : Quotient CKMMatrixSetoid) : ℝ :=
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else VcbAbs V / √ (VudAbs V ^ 2 + VusAbs V ^ 2)
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/-- Given a CKM matrix `V` the real number corresponding to `θ₁₂` in the
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standard parameterization. --/
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standard parameterization. --/
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def θ₁₂ (V : Quotient CKMMatrixSetoid) : ℝ := Real.arcsin (S₁₂ V)
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/-- Given a CKM matrix `V` the real number corresponding to `θ₁₃` in the
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standard parameterization. --/
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standard parameterization. --/
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def θ₁₃ (V : Quotient CKMMatrixSetoid) : ℝ := Real.arcsin (S₁₃ V)
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/-- Given a CKM matrix `V` the real number corresponding to `θ₂₃` in the
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standard parameterization. --/
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standard parameterization. --/
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def θ₂₃ (V : Quotient CKMMatrixSetoid) : ℝ := Real.arcsin (S₂₃ V)
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/-- Given a CKM matrix `V` the real number corresponding to `cos θ₁₂` in the
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standard parameterization. --/
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standard parameterization. --/
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def C₁₂ (V : Quotient CKMMatrixSetoid) : ℝ := Real.cos (θ₁₂ V)
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/-- Given a CKM matrix `V` the real number corresponding to `cos θ₁₃` in the
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@ -60,7 +60,7 @@ standard parameterization. --/
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def C₁₃ (V : Quotient CKMMatrixSetoid) : ℝ := Real.cos (θ₁₃ V)
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/-- Given a CKM matrix `V` the real number corresponding to `sin θ₂₃` in the
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standard parameterization. --/
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standard parameterization. --/
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def C₂₃ (V : Quotient CKMMatrixSetoid) : ℝ := Real.cos (θ₂₃ V)
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/-- Given a CKM matrix `V` the real number corresponding to the phase `δ₁₃` in the
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@ -126,7 +126,7 @@ lemma S₂₃_leq_one (V : Quotient CKMMatrixSetoid) : S₂₃ V ≤ 1 := by
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lemma S₁₂_eq_sin_θ₁₂ (V : Quotient CKMMatrixSetoid) : Real.sin (θ₁₂ V) = S₁₂ V :=
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Real.sin_arcsin (le_trans (by simp) (S₁₂_nonneg V)) (S₁₂_leq_one V)
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lemma S₁₃_eq_sin_θ₁₃ (V : Quotient CKMMatrixSetoid) : Real.sin (θ₁₃ V) = S₁₃ V :=
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lemma S₁₃_eq_sin_θ₁₃ (V : Quotient CKMMatrixSetoid) : Real.sin (θ₁₃ V) = S₁₃ V :=
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Real.sin_arcsin (le_trans (by simp) (S₁₃_nonneg V)) (S₁₃_leq_one V)
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lemma S₂₃_eq_sin_θ₂₃ (V : Quotient CKMMatrixSetoid) : Real.sin (θ₂₃ V) = S₂₃ V :=
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@ -168,7 +168,7 @@ lemma S₂₃_of_Vub_eq_one {V : Quotient CKMMatrixSetoid} (ha : VubAbs V = 1) :
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rw [S₂₃, if_pos ha]
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lemma S₂₃_of_Vub_neq_one {V : Quotient CKMMatrixSetoid} (ha : VubAbs V ≠ 1) :
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S₂₃ V = VcbAbs V / √ (VudAbs V ^ 2 + VusAbs V ^ 2) := by
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S₂₃ V = VcbAbs V / √ (VudAbs V ^ 2 + VusAbs V ^ 2) := by
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rw [S₂₃, if_neg ha]
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end sines
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@ -336,9 +336,9 @@ namespace standParam
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open Invariant
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lemma mulExpδ₁₃_on_param_δ₁₃ (V : CKMMatrix) (δ₁₃ : ℝ) :
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mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ =
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mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ =
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sin (θ₁₂ ⟦V⟧) * cos (θ₁₃ ⟦V⟧) ^ 2 * sin (θ₂₃ ⟦V⟧) * sin (θ₁₃ ⟦V⟧)
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* cos (θ₁₂ ⟦V⟧) * cos (θ₂₃ ⟦V⟧) * cexp (I * δ₁₃) := by
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* cos (θ₁₂ ⟦V⟧) * cos (θ₂₃ ⟦V⟧) * cexp (I * δ₁₃) := by
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refine mulExpδ₁₃_eq _ _ _ _ ?_ ?_ ?_ ?_
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rw [S₁₂_eq_sin_θ₁₂]
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exact S₁₂_nonneg _
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@ -364,7 +364,7 @@ lemma mulExpδ₁₃_on_param_eq_zero_iff (V : CKMMatrix) (δ₁₃ : ℝ) :
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aesop
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lemma mulExpδ₁₃_on_param_abs (V : CKMMatrix) (δ₁₃ : ℝ) :
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Complex.abs (mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) =
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Complex.abs (mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) =
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sin (θ₁₂ ⟦V⟧) * cos (θ₁₃ ⟦V⟧) ^ 2 * sin (θ₂₃ ⟦V⟧) * sin (θ₁₃ ⟦V⟧)
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* cos (θ₁₂ ⟦V⟧) * cos (θ₂₃ ⟦V⟧) := by
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rw [mulExpδ₁₃_on_param_δ₁₃]
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@ -373,19 +373,19 @@ lemma mulExpδ₁₃_on_param_abs (V : CKMMatrix) (δ₁₃ : ℝ) :
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complexAbs_sin_θ₂₃, complexAbs_cos_θ₂₃]
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lemma mulExpδ₁₃_on_param_neq_zero_arg (V : CKMMatrix) (δ₁₃ : ℝ)
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(h1 : mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ ≠ 0 ) :
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(h1 : mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ ≠ 0 ) :
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cexp (arg ( mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ ) * I) =
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cexp (δ₁₃ * I) := by
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have h1a := mulExpδ₁₃_on_param_δ₁₃ V δ₁₃
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have habs := mulExpδ₁₃_on_param_abs V δ₁₃
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have h2 : mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ = Complex.abs
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(mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) * exp (δ₁₃ * I) := by
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have h2 : mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ = Complex.abs
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(mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) * exp (δ₁₃ * I) := by
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rw [habs, h1a]
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ring_nf
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nth_rewrite 1 [← abs_mul_exp_arg_mul_I (mulExpδ₁₃
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⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ )] at h2
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have habs_neq_zero :
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(Complex.abs (mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) : ℂ) ≠ 0 := by
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(Complex.abs (mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧) : ℂ) ≠ 0 := by
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simp only [ne_eq, ofReal_eq_zero, map_eq_zero]
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exact h1
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rw [← mul_right_inj' habs_neq_zero]
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@ -514,7 +514,7 @@ lemma eq_standParam_of_fstRowThdColRealCond {V : CKMMatrix} (hb : [V]ud ≠ 0
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funext i
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fin_cases i
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simp only [uRow, Fin.isValue, Fin.zero_eta, cons_val_zero, standParam, standParamAsMatrix,
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ofReal_cos, ofReal_sin, ofReal_neg, mul_neg, neg_mul, neg_neg, cons_val', empty_val',
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ofReal_cos, ofReal_sin, ofReal_neg, mul_neg, neg_mul, neg_neg, cons_val', empty_val',
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cons_val_fin_one, cons_val_one, head_cons, cons_val_two, tail_cons]
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rw [hV.1, VudAbs_eq_C₁₂_mul_C₁₃ ⟦V⟧]
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simp [C₁₂, C₁₃]
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@ -613,7 +613,7 @@ theorem exists_δ₁₃ (V : CKMMatrix) :
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rw [hUV] at hna
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simp [VAbs] at hna
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simp_all
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have hU' := eq_standParam_of_fstRowThdColRealCond haU hU.2
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have hU' := eq_standParam_of_fstRowThdColRealCond haU hU.2
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rw [hU'] at hU
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use (- arg ([U]ub))
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rw [← hUV]
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@ -639,7 +639,7 @@ theorem eq_standardParameterization_δ₃ (V : CKMMatrix) :
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obtain ⟨δ₁₃', hδ₃⟩ := exists_δ₁₃ V
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have hSV := (Quotient.eq.mpr (hδ₃))
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by_cases h : Invariant.mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃'⟧ ≠ 0
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have h2 := eq_exp_of_phases (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃'
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have h2 := eq_exp_of_phases (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃'
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(δ₁₃ ⟦V⟧) (by rw [← mulExpδ₁₃_on_param_neq_zero_arg V δ₁₃' h, ← hSV, δ₁₃, Invariant.mulExpδ₁₃])
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rw [h2] at hδ₃
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exact hδ₃
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