Line In Cubic expand
PureU1.Odd.lineInCubic_expand
Plain-language statement
The condition that a linear solution sits on a line between the two planes within the cubic expands into a on accCubeTriLinSymm applied to the points within the planes.
Exact Lean statement
lemma lineInCubic_expand {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S) :
∀ (g : Fin n → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f) (a b : ℚ),
3 * a * b * (a * accCubeTriLinSymm (P g) (P g) (P! f)
+ b * accCubeTriLinSymm (P! f) (P! f) (P g)) = 0Formal artifact
Lean source
lemma lineInCubic_expand {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S) : ∀ (g : Fin n → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f) (a b : ℚ), 3 * a * b * (a * accCubeTriLinSymm (P g) (P g) (P! f) + b * accCubeTriLinSymm (P! f) (P! f) (P g)) = 0 := by intro g f hS a b have h1 := h g f hS a b change accCubeTriLinSymm.toCubic (a • P g + b • P! f) = 0 at h1 simp only [TriLinearSymm.toCubic_add, HomogeneousCubic.map_smul, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1 erw [P_accCube, P!_accCube] at h1 linear_combination h1- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QFT/QED/AnomalyCancellation/Odd/LineInCubic.lean:45-55
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