Constant EB smooth
Electromagnetism.ElectromagneticPotential.constantEB_smooth
Project documentation
An electric potential which gives a given constant E-field and B-field. -/ @[nolint unusedArguments] noncomputable def constantEB {d : ℕ} (c : SpeedOfLight) (E₀ : EuclideanSpace ℝ (Fin d)) (B₀ : Fin d × Fin d → ℝ) (B₀_antisymm : ∀ i j, B₀ (i, j) = - B₀ (j, i)) : ElectromagneticPotential d where val := fun x μ => match μ with | Sum.inl _ => - (1/c) * ⟪E₀,...
Exact Lean statement
lemma constantEB_smooth {c : SpeedOfLight}
{E₀ : EuclideanSpace ℝ (Fin d)} {B₀ : Fin d × Fin d → ℝ}
{B₀_antisymm : ∀ i j, B₀ (i, j) = - B₀ (j, i)} :
ContDiff ℝ ∞ (constantEB c E₀ B₀ B₀_antisymm)Formal artifact
Lean source
lemma constantEB_smooth {c : SpeedOfLight} {E₀ : EuclideanSpace ℝ (Fin d)} {B₀ : Fin d × Fin d → ℝ} {B₀_antisymm : ∀ i j, B₀ (i, j) = - B₀ (j, i)} : ContDiff ℝ ∞ (constantEB c E₀ B₀ B₀_antisymm) := by rw [← Lorentz.Vector.contDiff_apply] intro μ match μ with | Sum.inl _ => simp [constantEB] apply ContDiff.neg apply ContDiff.mul · fun_prop apply ContDiff.inner · fun_prop · fun_prop | Sum.inr i => simp [constantEB] apply ContDiff.mul · fun_prop · apply ContDiff.sum intro j _ apply ContDiff.mul · fun_prop fun_prop- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Electromagnetism/Vacuum/Constant.lean:85-108
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