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refactor: Lint

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jstoobysmith 2024-07-19 17:00:32 -04:00
parent 52e591fa7a
commit 9f27a3a9fd
46 changed files with 176 additions and 168 deletions
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12
HepLean/AnomalyCancellation/PureU1/Even/LineInCubic.lean
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@ -49,23 +49,23 @@ lemma lineInCubic_expand {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic S)
change accCubeTriLinSymm.toCubic (a • P g + b • P! f) = 0 at h1
simp only [TriLinearSymm.toCubic_add] at h1
simp only [HomogeneousCubic.map_smul,
accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1
accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1
erw [P_accCube, P!_accCube] at h1
rw [← h1]
ring
/--
This lemma states that for a given `S` of type `(PureU1 (2 * n.succ)).AnomalyFreeLinear` and
a proof `h` that the line through `S` lies on a cubic curve,
for any functions `g : Fin n.succ → ℚ` and `f : Fin n → ℚ`, if `S.val = P g + P! f`,
then `accCubeTriLinSymm.toFun (P g, P g, P! f) = 0`.
This lemma states that for a given `S` of type `(PureU1 (2 * n.succ)).AnomalyFreeLinear` and
a proof `h` that the line through `S` lies on a cubic curve,
for any functions `g : Fin n.succ → ℚ` and `f : Fin n → ℚ`, if `S.val = P g + P! f`,
then `accCubeTriLinSymm.toFun (P g, P g, P! f) = 0`.
-/
lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic S) :
∀ (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
intro g f hS
linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1) -
(lineInCubic_expand h g f hS 1 2) / 6
(lineInCubic_expand h g f hS 1 2) / 6
/-- A `LinSol` satisfies `LineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
def LineInCubicPerm (S : (PureU1 (2 * n.succ)).LinSols) : Prop :=