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refactor: replace simps

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jstoobysmith 2024-08-30 11:52:27 -04:00
parent 81f3566be8
commit cd04e13ced
6 changed files with 43 additions and 45 deletions
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12
HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/StandardParameters.lean
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@ -489,7 +489,7 @@ lemma eq_standParam_of_fstRowThdColRealCond {V : CKMMatrix} (hb : [V]ud ≠ 0
(hV : FstRowThdColRealCond V) : V = standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) (- arg [V]ub) := by
have hb' : VubAbs ⟦V⟧ ≠ 1 := by
rw [ud_us_neq_zero_iff_ub_neq_one] at hb
simp [VAbs, hb]
exact hb
have h1 : ofReal (√(VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2) *
↑√(VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2)) = ofReal (VAbs 0 0 ⟦V⟧ ^ 2 + VAbs 0 1 ⟦V⟧ ^ 2) := by
rw [Real.mul_self_sqrt]
@ -552,16 +552,16 @@ lemma eq_standParam_of_ubOnePhaseCond {V : CKMMatrix} (hV : ubOnePhaseCond V) :
have h1 : VubAbs ⟦V⟧ = 1 := by
simp [VAbs]
rw [hV.2.2.2.1]
simp
exact AbsoluteValue.map_one Complex.abs
refine eq_rows V ?_ ?_ hV.2.2.2.2.1
· funext i
fin_cases i
· simp [uRow, standParam, standParamAsMatrix]
rw [C₁₃_eq_ℂcos_θ₁₃ ⟦V⟧, C₁₃_of_Vub_eq_one h1, hV.1]
simp only [ofReal_zero, mul_zero]
exact Eq.symm (mul_eq_zero_of_right (cos ↑(θ₁₂ ⟦V⟧)) rfl)
· simp [uRow, standParam, standParamAsMatrix]
rw [C₁₃_eq_ℂcos_θ₁₃ ⟦V⟧, C₁₃_of_Vub_eq_one h1, hV.2.1]
simp only [ofReal_zero, mul_zero]
exact Eq.symm (mul_eq_zero_of_right (sin ↑(θ₁₂ ⟦V⟧)) rfl)
· simp [uRow, standParam, standParamAsMatrix]
rw [S₁₃_eq_ℂsin_θ₁₃ ⟦V⟧, S₁₃]
simp [VAbs]
@ -589,7 +589,7 @@ lemma eq_standParam_of_ubOnePhaseCond {V : CKMMatrix} (hV : ubOnePhaseCond V) :
rw [h3, S₂₃_of_Vub_eq_one h1, hV.2.2.2.2.2.2]
· simp [cRow, standParam, standParamAsMatrix]
rw [C₁₃_eq_ℂcos_θ₁₃ ⟦V⟧, C₁₃_of_Vub_eq_one h1, hV.2.2.1]
simp
exact Eq.symm (mul_eq_zero_of_right (sin ↑(θ₂₃ ⟦V⟧)) rfl)
theorem exists_δ₁₃ (V : CKMMatrix) :
∃ (δ₃ : ℝ), V ≈ standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₃ := by
@ -639,7 +639,7 @@ theorem eq_standardParameterization_δ₃ (V : CKMMatrix) :
· simp at h
have h1 : δ₁₃ ⟦V⟧ = 0 := by
rw [hSV, δ₁₃, h]
simp
exact arg_zero
rw [h1]
rw [mulExpδ₁₃_on_param_eq_zero_iff, Vs_zero_iff_cos_sin_zero] at h
refine phaseShiftRelation_equiv.trans hδ₃ ?_