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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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32
HepLean/AnomalyCancellation/MSSMNu/Basic.lean
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@ -43,7 +43,7 @@ def toSMPlusH : MSSMCharges.Charges ≃ (Fin 18 ⊕ Fin 2 → ℚ) :=
@[simps!]
def splitSMPlusH : (Fin 18 ⊕ Fin 2 → ℚ) ≃ (Fin 18 → ℚ) × (Fin 2 → ℚ) where
toFun f := (f ∘ Sum.inl , f ∘ Sum.inr)
invFun f := Sum.elim f.1 f.2
invFun f := Sum.elim f.1 f.2
left_inv f := Sum.elim_comp_inl_inr f
right_inv _ := rfl
@ -107,7 +107,7 @@ def Hu : MSSMCharges.Charges →ₗ[ℚ] ℚ where
map_smul' _ _ := by rfl
lemma charges_eq_toSpecies_eq (S T : MSSMCharges.Charges) :
S = T ↔ (∀ i, toSMSpecies i S = toSMSpecies i T) ∧ Hd S = Hd T ∧ Hu S = Hu T := by
S = T ↔ (∀ i, toSMSpecies i S = toSMSpecies i T) ∧ Hd S = Hd T ∧ Hu S = Hu T := by
apply Iff.intro
intro h
rw [h]
@ -159,7 +159,7 @@ def accGrav : MSSMCharges.Charges →ₗ[ℚ] ℚ where
/-- Extensionality lemma for `accGrav`. -/
lemma accGrav_ext {S T : MSSMCharges.Charges}
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i)
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i)
(hd : Hd S = Hd T) (hu : Hu S = Hu T) :
accGrav S = accGrav T := by
simp only [accGrav, MSSMSpecies_numberCharges, toSMSpecies_apply, Fin.isValue,
@ -192,7 +192,7 @@ def accSU2 : MSSMCharges.Charges →ₗ[ℚ] ℚ where
/-- Extensionality lemma for `accSU2`. -/
lemma accSU2_ext {S T : MSSMCharges.Charges}
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i)
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i)
(hd : Hd S = Hd T) (hu : Hu S = Hu T) :
accSU2 S = accSU2 T := by
simp only [accSU2, MSSMSpecies_numberCharges, toSMSpecies_apply, Fin.isValue,
@ -224,7 +224,7 @@ def accSU3 : MSSMCharges.Charges →ₗ[ℚ] ℚ where
/-- Extensionality lemma for `accSU3`. -/
lemma accSU3_ext {S T : MSSMCharges.Charges}
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i) :
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i) :
accSU3 S = accSU3 T := by
simp only [accSU3, MSSMSpecies_numberCharges, toSMSpecies_apply, Fin.isValue, LinearMap.coe_mk,
AddHom.coe_mk]
@ -256,7 +256,7 @@ def accYY : MSSMCharges.Charges →ₗ[ℚ] ℚ where
/-- Extensionality lemma for `accGrav`. -/
lemma accYY_ext {S T : MSSMCharges.Charges}
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i)
(hj : ∀ (j : Fin 6), ∑ i, (toSMSpecies j) S i = ∑ i, (toSMSpecies j) T i)
(hd : Hd S = Hd T) (hu : Hu S = Hu T) :
accYY S = accYY T := by
simp only [accYY, MSSMSpecies_numberCharges, toSMSpecies_apply, Fin.isValue,
@ -269,9 +269,9 @@ lemma accYY_ext {S T : MSSMCharges.Charges}
/-- The symmetric bilinear function used to define the quadratic ACC. -/
@[simps!]
def quadBiLin : BiLinearSymm MSSMCharges.Charges := BiLinearSymm.mk₂ (
fun (S, T) => ∑ i, (Q S i * Q T i + (- 2) * (U S i * U T i) +
D S i * D T i + (- 1) * (L S i * L T i) + E S i * E T i) +
def quadBiLin : BiLinearSymm MSSMCharges.Charges := BiLinearSymm.mk₂ (
fun (S, T) => ∑ i, (Q S i * Q T i + (- 2) * (U S i * U T i) +
D S i * D T i + (- 1) * (L S i * L T i) + E S i * E T i) +
(- Hd S * Hd T + Hu S * Hu T))
(by
intro a S T
@ -346,7 +346,7 @@ def cubeTriLinToFun
+ (2 * Hd S.1 * Hd S.2.1 * Hd S.2.2
+ 2 * Hu S.1 * Hu S.2.1 * Hu S.2.2)
lemma cubeTriLinToFun_map_smul₁ (a : ℚ) (S T R : MSSMCharges.Charges) :
lemma cubeTriLinToFun_map_smul₁ (a : ℚ) (S T R : MSSMCharges.Charges) :
cubeTriLinToFun (a • S, T, R) = a * cubeTriLinToFun (S, T, R) := by
simp only [cubeTriLinToFun]
rw [mul_add]
@ -366,7 +366,7 @@ lemma cubeTriLinToFun_map_add₁ (S T R L : MSSMCharges.Charges) :
rw [add_assoc, ← add_assoc (2 * Hd S * Hd R * Hd L + 2 * Hu S * Hu R * Hu L) _ _]
rw [add_comm (2 * Hd S * Hd R * Hd L + 2 * Hu S * Hu R * Hu L) _]
rw [add_assoc]
rw [← add_assoc _ _ (2 * Hd S * Hd R * Hd L + 2 * Hu S * Hu R * Hu L +
rw [← add_assoc _ _ (2 * Hd S * Hd R * Hd L + 2 * Hu S * Hu R * Hu L +
(2 * Hd T * Hd R * Hd L + 2 * Hu T * Hu R * Hu L))]
congr 1
rw [← Finset.sum_add_distrib]
@ -415,7 +415,7 @@ def accCube : HomogeneousCubic MSSMCharges.Charges := cubeTriLin.toCubic
lemma accCube_ext {S T : MSSMCharges.Charges}
(h : ∀ j, ∑ i, ((fun a => a^3) ∘ toSMSpecies j S) i =
∑ i, ((fun a => a^3) ∘ toSMSpecies j T) i)
(hd : Hd S = Hd T) (hu : Hu S = Hu T) :
(hd : Hd S = Hd T) (hu : Hu S = Hu T) :
accCube S = accCube T := by
simp only [HomogeneousCubic, accCube, cubeTriLin, TriLinearSymm.toCubic_apply,
TriLinearSymm.mk₃_toFun_apply_apply, cubeTriLinToFun]
@ -452,7 +452,7 @@ def MSSMACC : ACCSystem where
namespace MSSMACC
open MSSMCharges
lemma quadSol (S : MSSMACC.QuadSols) : accQuad S.val = 0 := by
lemma quadSol (S : MSSMACC.QuadSols) : accQuad S.val = 0 := by
have hS := S.quadSol
simp only [MSSMACC_numberQuadratic, HomogeneousQuadratic, MSSMACC_quadraticACCs] at hS
exact hS 0
@ -516,9 +516,9 @@ lemma AnomalyFreeMk''_val (S : MSSMACC.QuadSols)
/-- The dot product on the vector space of charges. -/
@[simps!]
def dot : BiLinearSymm MSSMCharges.Charges := BiLinearSymm.mk₂
(fun S => ∑ i, (Q S.1 i * Q S.2 i + U S.1 i * U S.2 i +
D S.1 i * D S.2 i + L S.1 i * L S.2 i + E S.1 i * E S.2 i
def dot : BiLinearSymm MSSMCharges.Charges := BiLinearSymm.mk₂
(fun S => ∑ i, (Q S.1 i * Q S.2 i + U S.1 i * U S.2 i +
D S.1 i * D S.2 i + L S.1 i * L S.2 i + E S.1 i * E S.2 i
+ N S.1 i * N S.2 i) + Hd S.1 * Hd S.2 + Hu S.1 * Hu S.2)
(by
intro a S T