refactor: Lint

This commit is contained in:
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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@ -36,7 +36,7 @@ open minkowskiMetric in
/-- The Lorentz group is the subset of matrices which preserve the minkowski metric. -/
def LorentzGroup (d : ) : Set (Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ) :=
{Λ : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) |
∀ (x y : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ y⟫ₘ = ⟪x, y⟫ₘ}
∀ (x y : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ y⟫ₘ = ⟪x, y⟫ₘ}
namespace LorentzGroup
/-- Notation for the Lorentz group. -/

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@ -145,7 +145,7 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
smul_eq_mul, LinearMap.neg_apply]
field_simp
rw [u.1.2, v.1.2, minkowskiMetric.symm v.1.1 u, minkowskiMetric.symm u y,
minkowskiMetric.symm v y]
minkowskiMetric.symm v y]
ring
/-- A generalised boost as an element of the Lorentz Group. -/

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@ -63,7 +63,7 @@ lemma not_orthochronous_iff_le_zero :
/-- The continuous map taking a Lorentz transformation to its `0 0` element. -/
def timeCompCont : C(LorentzGroup d, ) := ⟨fun Λ => timeComp Λ,
Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
/-- An auxillary function used in the definition of `orthchroMapReal`. -/
def stepFunction : := fun t =>
@ -72,7 +72,7 @@ def stepFunction : := fun t =>
lemma stepFunction_continuous : Continuous stepFunction := by
apply Continuous.if ?_ continuous_const (Continuous.if ?_ continuous_const continuous_id)
<;> intro a ha
<;> intro a ha
rw [@Set.Iic_def, @frontier_Iic, @Set.mem_singleton_iff] at ha
rw [ha]
simp [neg_lt_self_iff, zero_lt_one, ↓reduceIte]
@ -157,7 +157,7 @@ def orthchroRep : LorentzGroup d →* ℤ₂ where
map_mul' Λ Λ' := by
simp only
by_cases h : IsOrthochronous Λ
<;> by_cases h' : IsOrthochronous Λ'
<;> by_cases h' : IsOrthochronous Λ'
rw [orthchroMap_IsOrthochronous h, orthchroMap_IsOrthochronous h',
orthchroMap_IsOrthochronous (mul_othchron_of_othchron_othchron h h')]
rfl