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refactor: Remove double empty lines

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jstoobysmith 2024-07-03 07:56:30 -04:00
parent ae18a2196d
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16
HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/StandardParameters.lean
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@ -18,7 +18,6 @@ These, when used in the standard parameterization return `V` up to equivalence.
This leads to the theorem `standParam.exists_for_CKMatrix` which says that up to equivalence every
CKM matrix can be written using the standard parameterization.
-/
open Matrix Complex
open ComplexConjugate
@ -333,7 +332,6 @@ lemma Vs_zero_iff_cos_sin_zero (V : CKMMatrix) :
end VAbs
namespace standParam
open Invariant
@ -409,7 +407,6 @@ lemma on_param_cos_θ₁₃_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.c
rfl
rfl
lemma on_param_cos_θ₁₂_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.cos (θ₁₂ ⟦V⟧) = 0) :
standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃ ≈ standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) 0 := by
use 0, δ₁₃, δ₁₃, -δ₁₃, 0, - δ₁₃
@ -434,7 +431,6 @@ lemma on_param_cos_θ₁₂_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.c
ring_nf
field_simp
lemma on_param_cos_θ₂₃_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.cos (θ₂₃ ⟦V⟧) = 0) :
standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃ ≈ standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) 0 := by
use 0, δ₁₃, 0, 0, 0, - δ₁₃
@ -451,7 +447,6 @@ lemma on_param_cos_θ₂₃_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.c
ring
field_simp
lemma on_param_sin_θ₁₃_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.sin (θ₁₃ ⟦V⟧) = 0) :
standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃ ≈ standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) 0 := by
use 0, 0, 0, 0, 0, 0
@ -488,8 +483,6 @@ lemma on_param_sin_θ₁₂_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.s
ring_nf
field_simp
lemma on_param_sin_θ₂₃_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.sin (θ₂₃ ⟦V⟧) = 0) :
standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃ ≈ standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) 0 := by
use 0, 0, δ₁₃, 0, 0, - δ₁₃
@ -506,9 +499,6 @@ lemma on_param_sin_θ₂₃_eq_zero {V : CKMMatrix} (δ₁₃ : ℝ) (h : Real.s
ring
field_simp
lemma eq_standParam_of_fstRowThdColRealCond {V : CKMMatrix} (hb : [V]ud ≠ 0 ∨ [V]us ≠ 0)
(hV : FstRowThdColRealCond V) : V = standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) (- arg [V]ub) := by
have hb' : VubAbs ⟦V⟧ ≠ 1 := by
@ -565,7 +555,6 @@ lemma eq_standParam_of_fstRowThdColRealCond {V : CKMMatrix} (hb : [V]ud ≠ 0
rw [VcbAbs_eq_S₂₃_mul_C₁₃ ⟦V⟧, S₂₃_eq_ℂsin_θ₂₃ ⟦V⟧, C₁₃]
simp
lemma eq_standParam_of_ubOnePhaseCond {V : CKMMatrix} (hV : ubOnePhaseCond V) :
V = standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) 0 := by
have h1 : VubAbs ⟦V⟧ = 1 := by
@ -610,7 +599,6 @@ lemma eq_standParam_of_ubOnePhaseCond {V : CKMMatrix} (hV : ubOnePhaseCond V) :
rw [C₁₃_eq_ℂcos_θ₁₃ ⟦V⟧, C₁₃_of_Vub_eq_one h1, hV.2.2.1]
simp
theorem exists_δ₁₃ (V : CKMMatrix) :
∃ (δ₃ : ℝ), V ≈ standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₃ := by
obtain ⟨U, hU⟩ := fstRowThdColRealCond_holds_up_to_equiv V
@ -670,7 +658,6 @@ theorem eq_standardParameterization_δ₃ (V : CKMMatrix) :
exact on_param_sin_θ₁₃_eq_zero δ₁₃' h
exact on_param_sin_θ₂₃_eq_zero δ₁₃' h
theorem exists_for_CKMatrix (V : CKMMatrix) :
∃ (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ), V ≈ standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃ := by
use θ₁₂ ⟦V⟧, θ₁₃ ⟦V⟧, θ₂₃ ⟦V⟧, δ₁₃ ⟦V⟧
@ -678,9 +665,6 @@ theorem exists_for_CKMatrix (V : CKMMatrix) :
end standParam
open CKMMatrix
end