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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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8
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/Basic.lean
View file

@ -158,7 +158,7 @@ lemma cube_proj_proj_B₃ (T : MSSMACC.LinSols) :
lemma cube_proj_proj_self (T : MSSMACC.Sols) :
cubeTriLin (proj T.1.1).val (proj T.1.1).val T.val =
2 * dot Y₃.val B₃.val *
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
( dot Y₃.val T.val- 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
rw [proj_val]
rw [cubeTriLin.map_add₁, cubeTriLin.map_add₂]
@ -168,13 +168,13 @@ lemma cube_proj_proj_self (T : MSSMACC.Sols) :
repeat rw [cubeTriLin.map_add₂]
repeat rw [cubeTriLin.map_smul₂]
erw [T.cubicSol]
rw [cubeTriLin.swap₁ Y₃.val T.val T.val, cubeTriLin.swap₂ T.val Y₃.val T.val]
rw [cubeTriLin.swap₁ B₃.val T.val T.val, cubeTriLin.swap₂ T.val B₃.val T.val]
rw [cubeTriLin.swap₁ Y₃.val T.val T.val, cubeTriLin.swap₂ T.val Y₃.val T.val]
rw [cubeTriLin.swap₁ B₃.val T.val T.val, cubeTriLin.swap₂ T.val B₃.val T.val]
ring
lemma cube_proj (T : MSSMACC.Sols) :
cubeTriLin (proj T.1.1).val (proj T.1.1).val (proj T.1.1).val =
3 * dot Y₃.val B₃.val ^ 2 *
3 * dot Y₃.val B₃.val ^ 2 *
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
nth_rewrite 3 [proj_val]

16
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/PlaneWithY3B3.lean
View file

@ -42,7 +42,7 @@ lemma planeY₃B₃_smul (R : MSSMACC.AnomalyFreePerp) (a b c d : ℚ) :
rw [smul_add, smul_add]
rw [smul_smul, smul_smul, smul_smul]
lemma planeY₃B₃_eq (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) (h : a = a' ∧ b = b' ∧ c = c') :
lemma planeY₃B₃_eq (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) (h : a = a' ∧ b = b' ∧ c = c') :
(planeY₃B₃ R a b c) = (planeY₃B₃ R a' b' c') := by
rw [h.1, h.2.1, h.2.2]
@ -82,7 +82,7 @@ lemma planeY₃B₃_val_eq' (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) (hR' : R
have h2 := congrArg (fun S => S i) h1i
change _ = 0 at h2
simp [HSMul.hSMul] at h2
have hc : c + -c' = 0 := by
have hc : c + -c' = 0 := by
cases h2 <;> rename_i h2
exact h2
exact (hi h2).elim
@ -105,8 +105,8 @@ lemma planeY₃B₃_quad (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) :
lemma planeY₃B₃_cubic (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) :
accCube (planeY₃B₃ R a b c).val = c ^ 2 *
(3 * a * cubeTriLin R.val R.val Y₃.val
+ 3 * b * cubeTriLin R.val R.val B₃.val + c * cubeTriLin R.val R.val R.val) := by
(3 * a * cubeTriLin R.val R.val Y₃.val
+ 3 * b * cubeTriLin R.val R.val B₃.val + c * cubeTriLin R.val R.val R.val) := by
rw [planeY₃B₃_val]
erw [TriLinearSymm.toCubic_add]
erw [lineY₃B₃Charges_cubic]
@ -178,7 +178,7 @@ def lineCube (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :
MSSMACC.LinSols :=
planeY₃B₃ R
(a₂ * cubeTriLin R.val R.val R.val - 3 * a₃ * cubeTriLin R.val R.val B₃.val)
(3 * a₃ * cubeTriLin R.val R.val Y₃.val - a₁ * cubeTriLin R.val R.val R.val)
(3 * a₃ * cubeTriLin R.val R.val Y₃.val - a₁ * cubeTriLin R.val R.val R.val)
(3 * (a₁ * cubeTriLin R.val R.val B₃.val - a₂ * cubeTriLin R.val R.val Y₃.val))
lemma lineCube_smul (R : MSSMACC.AnomalyFreePerp) (a b c d : ℚ) :
@ -205,7 +205,7 @@ lemma lineCube_quad (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :
section proj
lemma α₃_proj (T : MSSMACC.Sols) : α₃ (proj T.1.1) =
lemma α₃_proj (T : MSSMACC.Sols) : α₃ (proj T.1.1) =
6 * dot Y₃.val B₃.val ^ 3 * (
cubeTriLin T.val T.val Y₃.val * quadBiLin B₃.val T.val -
cubeTriLin T.val T.val B₃.val * quadBiLin Y₃.val T.val) := by
@ -214,13 +214,13 @@ lemma α₃_proj (T : MSSMACC.Sols) : α₃ (proj T.1.1) =
ring
lemma α₂_proj (T : MSSMACC.Sols) : α₂ (proj T.1.1) =
- α₃ (proj T.1.1) * (dot Y₃.val T.val - 2 * dot B₃.val T.val) := by
- α₃ (proj T.1.1) * (dot Y₃.val T.val - 2 * dot B₃.val T.val) := by
rw [α₃_proj, α₂]
rw [cube_proj_proj_Y₃, quad_Y₃_proj, quad_proj, cube_proj]
ring
lemma α₁_proj (T : MSSMACC.Sols) : α₁ (proj T.1.1) =
- α₃ (proj T.1.1) * (dot B₃.val T.val - dot Y₃.val T.val) := by
- α₃ (proj T.1.1) * (dot B₃.val T.val - dot Y₃.val T.val) := by
rw [α₃_proj, α₁]
rw [cube_proj_proj_B₃, quad_B₃_proj, quad_proj, cube_proj]
ring

12
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean
View file

@ -146,7 +146,7 @@ def InCubeSolProp (R : MSSMACC.Sols) : Prop :=
/-- A rational which has two properties. It is zero for a solution `T` if and only if
that solution satisfies `inCubeSolProp`. It appears in the definition of `inLineEqProj`. -/
def cubicCoeff (T : MSSMACC.Sols) : ℚ :=
3 * (dot Y₃.val B₃.val) ^ 3 * (cubeTriLin T.val T.val Y₃.val ^ 2 +
3 * (dot Y₃.val B₃.val) ^ 3 * (cubeTriLin T.val T.val Y₃.val ^ 2 +
cubeTriLin T.val T.val B₃.val ^ 2 )
lemma inCubeSolProp_iff_cubicCoeff_zero (T : MSSMACC.Sols) :
@ -243,7 +243,7 @@ def toSolNSProj (T : MSSMACC.Sols) : MSSMACC.AnomalyFreePerp × ℚ × ℚ ×
lemma toSolNS_proj (T : NotInLineEqSol) : toSolNS (toSolNSProj T.val) = T.val := by
apply ACCSystem.Sols.ext
rw [toSolNS, toSolNSProj]
change (lineEqCoeff T.val)⁻¹ • (toSolNSQuad _).1.1 = _
change (lineEqCoeff T.val)⁻¹ • (toSolNSQuad _).1.1 = _
rw [toSolNSQuad_eq_planeY₃B₃_on_α]
rw [planeY₃B₃_val]
rw [Y₃_plus_B₃_plus_proj]
@ -254,7 +254,7 @@ lemma toSolNS_proj (T : NotInLineEqSol) : toSolNS (toSolNSProj T.val) = T.val :=
rw [lineEqCoeff]
ring
rw [h1]
have h1 := (lineEqPropSol_iff_lineEqCoeff_zero T.val).mpr.mt T.prop
have h1 := (lineEqPropSol_iff_lineEqCoeff_zero T.val).mpr.mt T.prop
rw [← MulAction.mul_smul, mul_comm, mul_inv_cancel h1]
simp
@ -302,7 +302,7 @@ lemma inLineEqToSol_proj (T : InLineEqSol) : inLineEqToSol (inLineEqProj T) = T.
simp
/-- Given a element of `inQuad × ℚ × ℚ × ℚ`, a solution to the ACCs. -/
def inQuadToSol : InQuad × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a₁, a₂, a₃) =>
def inQuadToSol : InQuad × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a₁, a₂, a₃) =>
AnomalyFreeMk' (lineCube R.val.val a₁ a₂ a₃)
(by
erw [planeY₃B₃_quad]
@ -391,8 +391,8 @@ lemma inQuadCubeToSol_proj (T : InQuadCubeSol) :
/-- Given an element of `MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ` a solution. We will
show that this map is a surjection. -/
def toSol : MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a, b, c) =>
if h₃ : LineEqProp R ∧ InQuadProp R ∧ InCubeProp R then
def toSol : MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a, b, c) =>
if h₃ : LineEqProp R ∧ InQuadProp R ∧ InCubeProp R then
inQuadCubeToSol (⟨⟨⟨R, h₃.1⟩, h₃.2.1⟩, h₃.2.2⟩, a, b, c)
else
if h₂ : LineEqProp R ∧ InQuadProp R then