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refactor: Change case of type and props

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jstoobysmith 2024-06-26 11:54:02 -04:00
parent 18b83f582e
commit f7a638d32e
58 changed files with 695 additions and 696 deletions
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34
HepLean/AnomalyCancellation/SM/Basic.lean
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@ -36,17 +36,17 @@ variable {n : ℕ}
/-- An equivalence between the set `(SMCharges n).charges` and the set
`(Fin 5 → Fin n → ℚ)`. -/
@[simps!]
def toSpeciesEquiv : (SMCharges n).charges ≃ (Fin 5 → Fin n → ℚ) :=
def toSpeciesEquiv : (SMCharges n).Charges ≃ (Fin 5 → Fin n → ℚ) :=
((Equiv.curry _ _ _).symm.trans ((@finProdFinEquiv 5 n).arrowCongr (Equiv.refl ℚ))).symm
/-- For a given `i ∈ Fin 5`, the projection of a charge onto that species. -/
@[simps!]
def toSpecies (i : Fin 5) : (SMCharges n).charges →ₗ[ℚ] (SMSpecies n).charges where
def toSpecies (i : Fin 5) : (SMCharges n).Charges →ₗ[ℚ] (SMSpecies n).Charges where
toFun S := toSpeciesEquiv S i
map_add' _ _ := by rfl
map_smul' _ _ := by rfl
lemma charges_eq_toSpecies_eq (S T : (SMCharges n).charges) :
lemma charges_eq_toSpecies_eq (S T : (SMCharges n).Charges) :
S = T ↔ ∀ i, toSpecies i S = toSpecies i T := by
apply Iff.intro
exact fun a i => congrArg (⇑(toSpecies i)) a
@ -84,7 +84,7 @@ variable {n : ℕ}
/-- The gravitational anomaly equation. -/
@[simp]
def accGrav : (SMCharges n).charges →ₗ[ℚ] ℚ where
def accGrav : (SMCharges n).Charges →ₗ[ℚ] ℚ where
toFun S := ∑ i, (6 * Q S i + 3 * U S i + 3 * D S i + 2 * L S i + E S i)
map_add' S T := by
simp only
@ -102,7 +102,7 @@ def accGrav : (SMCharges n).charges →ₗ[ℚ] ℚ where
ring
/-- Extensionality lemma for `accGrav`. -/
lemma accGrav_ext {S T : (SMCharges n).charges}
lemma accGrav_ext {S T : (SMCharges n).Charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accGrav S = accGrav T := by
simp only [accGrav, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
@ -114,7 +114,7 @@ lemma accGrav_ext {S T : (SMCharges n).charges}
/-- The `SU(2)` anomaly equation. -/
@[simp]
def accSU2 : (SMCharges n).charges →ₗ[ℚ] ℚ where
def accSU2 : (SMCharges n).Charges →ₗ[ℚ] ℚ where
toFun S := ∑ i, (3 * Q S i + L S i)
map_add' S T := by
simp only
@ -132,7 +132,7 @@ def accSU2 : (SMCharges n).charges →ₗ[ℚ] ℚ where
ring
/-- Extensionality lemma for `accSU2`. -/
lemma accSU2_ext {S T : (SMCharges n).charges}
lemma accSU2_ext {S T : (SMCharges n).Charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accSU2 S = accSU2 T := by
simp only [accSU2, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
@ -143,7 +143,7 @@ lemma accSU2_ext {S T : (SMCharges n).charges}
/-- The `SU(3)` anomaly equations. -/
@[simp]
def accSU3 : (SMCharges n).charges →ₗ[ℚ] ℚ where
def accSU3 : (SMCharges n).Charges →ₗ[ℚ] ℚ where
toFun S := ∑ i, (2 * Q S i + U S i + D S i)
map_add' S T := by
simp only
@ -161,7 +161,7 @@ def accSU3 : (SMCharges n).charges →ₗ[ℚ] ℚ where
ring
/-- Extensionality lemma for `accSU3`. -/
lemma accSU3_ext {S T : (SMCharges n).charges}
lemma accSU3_ext {S T : (SMCharges n).Charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accSU3 S = accSU3 T := by
simp only [accSU3, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
@ -173,7 +173,7 @@ lemma accSU3_ext {S T : (SMCharges n).charges}
/-- The `Y²` anomaly equation. -/
@[simp]
def accYY : (SMCharges n).charges →ₗ[ℚ] ℚ where
def accYY : (SMCharges n).Charges →ₗ[ℚ] ℚ where
toFun S := ∑ i, (Q S i + 8 * U S i + 2 * D S i + 3 * L S i
+ 6 * E S i)
map_add' S T := by
@ -192,7 +192,7 @@ def accYY : (SMCharges n).charges →ₗ[ℚ] ℚ where
ring
/-- Extensionality lemma for `accYY`. -/
lemma accYY_ext {S T : (SMCharges n).charges}
lemma accYY_ext {S T : (SMCharges n).Charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accYY S = accYY T := by
simp only [accYY, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
@ -204,7 +204,7 @@ lemma accYY_ext {S T : (SMCharges n).charges}
/-- The quadratic bilinear map. -/
@[simps!]
def quadBiLin : BiLinearSymm (SMCharges n).charges := BiLinearSymm.mk₂
def quadBiLin : BiLinearSymm (SMCharges n).Charges := BiLinearSymm.mk₂
(fun S => ∑ i, (Q S.1 i * Q S.2 i +
- 2 * (U S.1 i * U S.2 i) +
D S.1 i * D S.2 i +
@ -238,11 +238,11 @@ def quadBiLin : BiLinearSymm (SMCharges n).charges := BiLinearSymm.mk₂
/-- The quadratic anomaly cancellation condition. -/
@[simp]
def accQuad : HomogeneousQuadratic (SMCharges n).charges :=
def accQuad : HomogeneousQuadratic (SMCharges n).Charges :=
(@quadBiLin n).toHomogeneousQuad
/-- Extensionality lemma for `accQuad`. -/
lemma accQuad_ext {S T : (SMCharges n).charges}
lemma accQuad_ext {S T : (SMCharges n).Charges}
(h : ∀ j, ∑ i, ((fun a => a^2) ∘ toSpecies j S) i =
∑ i, ((fun a => a^2) ∘ toSpecies j T) i) :
accQuad S = accQuad T := by
@ -258,7 +258,7 @@ lemma accQuad_ext {S T : (SMCharges n).charges}
/-- The trilinear function defining the cubic. -/
@[simps!]
def cubeTriLin : TriLinearSymm (SMCharges n).charges := TriLinearSymm.mk₃
def cubeTriLin : TriLinearSymm (SMCharges n).Charges := TriLinearSymm.mk₃
(fun S => ∑ i, (6 * ((Q S.1 i) * (Q S.2.1 i) * (Q S.2.2 i))
+ 3 * ((U S.1 i) * (U S.2.1 i) * (U S.2.2 i))
+ 3 * ((D S.1 i) * (D S.2.1 i) * (D S.2.2 i))
@ -301,10 +301,10 @@ def cubeTriLin : TriLinearSymm (SMCharges n).charges := TriLinearSymm.mk₃
/-- The cubic acc. -/
@[simp]
def accCube : HomogeneousCubic (SMCharges n).charges := cubeTriLin.toCubic
def accCube : HomogeneousCubic (SMCharges n).Charges := cubeTriLin.toCubic
/-- Extensionality lemma for `accCube`. -/
lemma accCube_ext {S T : (SMCharges n).charges}
lemma accCube_ext {S T : (SMCharges n).Charges}
(h : ∀ j, ∑ i, ((fun a => a^3) ∘ toSpecies j S) i =
∑ i, ((fun a => a^3) ∘ toSpecies j T) i) :
accCube S = accCube T := by