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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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28
HepLean/AnomalyCancellation/SMNu/Permutations.lean
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@ -26,26 +26,26 @@ open BigOperators
/-- The group of `Sₙ` permutations for each species. -/
@[simp]
def permGroup (n : ℕ) := Fin 6 → Equiv.Perm (Fin n)
def PermGroup (n : ℕ) := Fin 6 → Equiv.Perm (Fin n)
variable {n : ℕ}
@[simp]
instance : Group (permGroup n) := Pi.group
instance : Group (PermGroup n) := Pi.group
/-- The image of an element of `permGroup n` under the representation on charges. -/
@[simps!]
def chargeMap (f : permGroup n) : (SMνCharges n).charges →ₗ[ℚ] (SMνCharges n).charges where
def chargeMap (f : PermGroup n) : (SMνCharges n).Charges →ₗ[ℚ] (SMνCharges n).Charges where
toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i )
map_add' _ _ := rfl
map_smul' _ _ := rfl
/-- The representation of `(permGroup n)` acting on the vector space of charges. -/
@[simp]
def repCharges {n : ℕ} : Representation ℚ (permGroup n) (SMνCharges n).charges where
def repCharges {n : ℕ} : Representation ℚ (PermGroup n) (SMνCharges n).Charges where
toFun f := chargeMap f⁻¹
map_mul' f g := by
simp only [permGroup, mul_inv_rev]
simp only [PermGroup, mul_inv_rev]
apply LinearMap.ext
intro S
rw [charges_eq_toSpecies_eq]
@ -61,49 +61,49 @@ def repCharges {n : ℕ} : Representation ℚ (permGroup n) (SMνCharges n).char
erw [toSMSpecies_toSpecies_inv]
rfl
lemma repCharges_toSpecies (f : permGroup n) (S : (SMνCharges n).charges) (j : Fin 6) :
lemma repCharges_toSpecies (f : PermGroup n) (S : (SMνCharges n).Charges) (j : Fin 6) :
toSpecies j (repCharges f S) = toSpecies j S ∘ f⁻¹ j := by
erw [toSMSpecies_toSpecies_inv]
lemma toSpecies_sum_invariant (m : ℕ) (f : permGroup n) (S : (SMνCharges n).charges) (j : Fin 6) :
lemma toSpecies_sum_invariant (m : ℕ) (f : PermGroup n) (S : (SMνCharges n).Charges) (j : Fin 6) :
∑ i, ((fun a => a ^ m) ∘ toSpecies j (repCharges f S)) i =
∑ i, ((fun a => a ^ m) ∘ toSpecies j S) i := by
erw [repCharges_toSpecies]
change ∑ i : Fin n, ((fun a => a ^ m) ∘ _) (⇑(f⁻¹ _) i) = ∑ i : Fin n, ((fun a => a ^ m) ∘ _) i
refine Equiv.Perm.sum_comp _ _ _ ?_
simp only [permGroup, Fin.isValue, Pi.inv_apply, ne_eq, coe_univ, Set.subset_univ]
simp only [PermGroup, Fin.isValue, Pi.inv_apply, ne_eq, coe_univ, Set.subset_univ]
lemma accGrav_invariant (f : permGroup n) (S : (SMνCharges n).charges) :
lemma accGrav_invariant (f : PermGroup n) (S : (SMνCharges n).Charges) :
accGrav (repCharges f S) = accGrav S :=
accGrav_ext
(by simpa using toSpecies_sum_invariant 1 f S)
lemma accSU2_invariant (f : permGroup n) (S : (SMνCharges n).charges) :
lemma accSU2_invariant (f : PermGroup n) (S : (SMνCharges n).Charges) :
accSU2 (repCharges f S) = accSU2 S :=
accSU2_ext
(by simpa using toSpecies_sum_invariant 1 f S)
lemma accSU3_invariant (f : permGroup n) (S : (SMνCharges n).charges) :
lemma accSU3_invariant (f : PermGroup n) (S : (SMνCharges n).Charges) :
accSU3 (repCharges f S) = accSU3 S :=
accSU3_ext
(by simpa using toSpecies_sum_invariant 1 f S)
lemma accYY_invariant (f : permGroup n) (S : (SMνCharges n).charges) :
lemma accYY_invariant (f : PermGroup n) (S : (SMνCharges n).Charges) :
accYY (repCharges f S) = accYY S :=
accYY_ext
(by simpa using toSpecies_sum_invariant 1 f S)
lemma accQuad_invariant (f : permGroup n) (S : (SMνCharges n).charges) :
lemma accQuad_invariant (f : PermGroup n) (S : (SMνCharges n).Charges) :
accQuad (repCharges f S) = accQuad S :=
accQuad_ext
(toSpecies_sum_invariant 2 f S)
lemma accCube_invariant (f : permGroup n) (S : (SMνCharges n).charges) :
lemma accCube_invariant (f : PermGroup n) (S : (SMνCharges n).Charges) :
accCube (repCharges f S) = accCube S :=
accCube_ext
(by simpa using toSpecies_sum_invariant 3 f S)