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refactor: pass at removing double spaces

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jstoobysmith 2024-07-12 10:36:39 -04:00
parent 1fe51b2e04
commit 1133b883f3
19 changed files with 121 additions and 121 deletions
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12
HepLean/SpaceTime/LorentzGroup/Orthochronous.lean
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@ -39,7 +39,7 @@ lemma IsOrthochronous_iff_transpose :
IsOrthochronous Λ ↔ IsOrthochronous (transpose Λ) := by rfl
lemma IsOrthochronous_iff_ge_one :
IsOrthochronous Λ ↔ 1 ≤ timeComp Λ := by
IsOrthochronous Λ ↔ 1 ≤ timeComp Λ := by
rw [IsOrthochronous_iff_futurePointing, NormOneLorentzVector.FuturePointing.mem_iff,
NormOneLorentzVector.time_pos_iff]
simp only [time, toNormOneLorentzVector, timeVec, Fin.isValue]
@ -68,7 +68,7 @@ def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => timeComp Λ ,
/-- An auxillary function used in the definition of `orthchroMapReal`. -/
def stepFunction : ℝ → ℝ := fun t =>
if t ≤ -1 then -1 else
if 1 ≤ t then 1 else t
if 1 ≤ t then 1 else t
lemma stepFunction_continuous : Continuous stepFunction := by
apply Continuous.if ?_ continuous_const (Continuous.if ?_ continuous_const continuous_id)
@ -105,20 +105,20 @@ lemma orthchroMapReal_minus_one_or_one (Λ : LorentzGroup d) :
apply Or.inr $ orthchroMapReal_on_IsOrthochronous h
apply Or.inl $ orthchroMapReal_on_not_IsOrthochronous h
local notation "ℤ₂" => Multiplicative (ZMod 2)
local notation "ℤ₂" => Multiplicative (ZMod 2)
/-- A continuous map from `lorentzGroup` to `ℤ₂` whose kernal are the Orthochronous elements. -/
def orthchroMap : C(LorentzGroup d, ℤ₂) :=
ContinuousMap.comp coeForℤ₂ {
toFun := fun Λ => ⟨orthchroMapReal Λ, orthchroMapReal_minus_one_or_one Λ⟩,
continuous_toFun := Continuous.subtype_mk (ContinuousMap.continuous orthchroMapReal) _}
continuous_toFun := Continuous.subtype_mk (ContinuousMap.continuous orthchroMapReal) _}
lemma orthchroMap_IsOrthochronous {Λ : LorentzGroup d} (h : IsOrthochronous Λ) :
orthchroMap Λ = 1 := by
simp [orthchroMap, orthchroMapReal_on_IsOrthochronous h]
lemma orthchroMap_not_IsOrthochronous {Λ : LorentzGroup d} (h : ¬ IsOrthochronous Λ) :
orthchroMap Λ = Additive.toMul (1 : ZMod 2) := by
orthchroMap Λ = Additive.toMul (1 : ZMod 2) := by
simp [orthchroMap, orthchroMapReal_on_not_IsOrthochronous h]
rfl
@ -136,7 +136,7 @@ lemma mul_othchron_of_not_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h :
rw [IsOrthochronous, timeComp_mul]
exact NormOneLorentzVector.FuturePointing.metric_reflect_not_mem_not_mem h h'
lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h : IsOrthochronous Λ)
lemma mul_not_othchron_of_othchron_not_othchron {Λ Λ' : LorentzGroup d} (h : IsOrthochronous Λ)
(h' : ¬ IsOrthochronous Λ') : ¬ IsOrthochronous (Λ * Λ') := by
rw [not_orthochronous_iff_le_zero, timeComp_mul]
rw [IsOrthochronous_iff_transpose] at h