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reactor: Removal of double spaces

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jstoobysmith 2024-07-12 11:23:02 -04:00
parent ce92e1d649
commit 13f62a50eb
64 changed files with 550 additions and 546 deletions
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16
HepLean/FlavorPhysics/CKMMatrix/Basic.lean
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@ -27,7 +27,7 @@ noncomputable section
leading diagonal. -/
@[simp]
def phaseShiftMatrix (a b c : ℝ) : Matrix (Fin 3) (Fin 3) ℂ :=
![![cexp (I * a), 0, 0], ![0, cexp (I * b), 0], ![0, 0, cexp (I * c)]]
![![cexp (I * a), 0, 0], ![0, cexp (I * b), 0], ![0, 0, cexp (I * c)]]
lemma phaseShiftMatrix_one : phaseShiftMatrix 0 0 0 = 1 := by
ext i j
@ -49,7 +49,7 @@ lemma phaseShiftMatrix_mul (a b c d e f : ℝ) :
fin_cases i <;> fin_cases j <;>
simp [Matrix.mul_apply, Fin.sum_univ_three]
any_goals rw [mul_add, exp_add]
change cexp (I * ↑c) * 0 = 0
change cexp (I * ↑c) * 0 = 0
simp
/-- Given three real numbers `a b c` the unitary matrix with `exp (I * a)` etc on the
@ -161,7 +161,7 @@ lemma equiv (V : CKMMatrix) (a b c d e f : ℝ) :
rfl
lemma ud (V : CKMMatrix) (a b c d e f : ℝ) :
(phaseShiftApply V a b c d e f).1 0 0 = cexp (a * I + d * I) * V.1 0 0 := by
(phaseShiftApply V a b c d e f).1 0 0 = cexp (a * I + d * I) * V.1 0 0 := by
simp only [Fin.isValue, phaseShiftApply_coe]
rw [mul_apply, Fin.sum_univ_three]
rw [mul_apply, mul_apply, mul_apply, Fin.sum_univ_three, Fin.sum_univ_three, Fin.sum_univ_three]
@ -173,7 +173,7 @@ lemma ud (V : CKMMatrix) (a b c d e f : ℝ) :
ring_nf
lemma us (V : CKMMatrix) (a b c d e f : ℝ) :
(phaseShiftApply V a b c d e f).1 0 1 = cexp (a * I + e * I) * V.1 0 1 := by
(phaseShiftApply V a b c d e f).1 0 1 = cexp (a * I + e * I) * V.1 0 1 := by
simp only [Fin.isValue, phaseShiftApply_coe]
rw [mul_apply, Fin.sum_univ_three]
rw [mul_apply, mul_apply, mul_apply, Fin.sum_univ_three, Fin.sum_univ_three, Fin.sum_univ_three]
@ -184,7 +184,7 @@ lemma us (V : CKMMatrix) (a b c d e f : ℝ) :
ring_nf
lemma ub (V : CKMMatrix) (a b c d e f : ℝ) :
(phaseShiftApply V a b c d e f).1 0 2 = cexp (a * I + f * I) * V.1 0 2 := by
(phaseShiftApply V a b c d e f).1 0 2 = cexp (a * I + f * I) * V.1 0 2 := by
simp only [Fin.isValue, phaseShiftApply_coe]
rw [mul_apply, Fin.sum_univ_three]
rw [mul_apply, mul_apply, mul_apply, Fin.sum_univ_three, Fin.sum_univ_three, Fin.sum_univ_three]
@ -236,7 +236,7 @@ lemma td (V : CKMMatrix) (a b c d e f : ℝ) :
simp only [Fin.isValue, cons_val', cons_val_zero, empty_val', cons_val_fin_one, vecCons_const,
cons_val_two, tail_val', head_val', cons_val_one, head_cons, tail_cons, head_fin_const,
zero_mul, add_zero, mul_zero]
change (0 * _ + _ ) * _ + (0 * _ + _ ) * 0 = _
change (0 * _ + _ ) * _ + (0 * _ + _ ) * 0 = _
simp only [Fin.isValue, zero_mul, zero_add, mul_zero, add_zero]
rw [exp_add]
ring_nf
@ -272,7 +272,7 @@ end phaseShiftApply
def VAbs' (V : unitaryGroup (Fin 3) ℂ) (i j : Fin 3) : ℝ := Complex.abs (V i j)
lemma VAbs'_equiv (i j : Fin 3) (V U : CKMMatrix) (h : V ≈ U) :
VAbs' V i j = VAbs' U i j := by
VAbs' V i j = VAbs' U i j := by
simp only [VAbs']
obtain ⟨a, b, c, e, f, g, h⟩ := h
rw [h]
@ -288,7 +288,7 @@ lemma VAbs'_equiv (i j : Fin 3) (V U : CKMMatrix) (h : V ≈ U) :
all_goals change Complex.abs (0 * _ + _) = _
all_goals simp [Complex.abs_exp]
/-- The absolute value of the `(i,j)`th any representative of `⟦V⟧`. -/
/-- The absolute value of the `(i,j)`th any representative of `⟦V⟧`. -/
def VAbs (i j : Fin 3) : Quotient CKMMatrixSetoid → ℝ :=
Quotient.lift (fun V => VAbs' V i j) (VAbs'_equiv i j)