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refactor: Remove double empty lines

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jstoobysmith 2024-07-03 07:56:30 -04:00
parent ae18a2196d
commit f03d063c86
60 changed files with 0 additions and 232 deletions
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10
HepLean/SpaceTime/LorentzVector/NormOne.lean
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@ -63,7 +63,6 @@ lemma time_nonpos_iff : v.1.time ≤ 0 ↔ v.1.time ≤ - 1 := by
· intro h
linarith
lemma time_nonneg_iff : 0 ≤ v.1.time ↔ 1 ≤ v.1.time := by
apply Iff.intro
· intro h
@ -167,14 +166,12 @@ lemma metric_reflect_mem_mem (h : v ∈ FuturePointing d) (hw : w ∈ FuturePoin
apply le_trans (neg_le_abs _ : _ ≤ |⟪(v.1).space, (w.1).space⟫_ℝ|) ?_
exact abs_real_inner_le_norm (v.1).space (w.1).space
lemma metric_reflect_not_mem_not_mem (h : v ∉ FuturePointing d) (hw : w ∉ FuturePointing d) :
0 ≤ ⟪v.1, w.1.spaceReflection⟫ₘ := by
have h1 := metric_reflect_mem_mem ((not_mem_iff_neg v).mp h) ((not_mem_iff_neg w).mp hw)
apply le_of_le_of_eq h1 ?_
simp [neg]
lemma metric_reflect_mem_not_mem (h : v ∈ FuturePointing d) (hw : w ∉ FuturePointing d) :
⟪v.1, w.1.spaceReflection⟫ₘ ≤ 0 := by
rw [show (0 : ℝ) = - 0 from zero_eq_neg.mpr rfl, le_neg]
@ -209,7 +206,6 @@ noncomputable def timeVecNormOneFuture : FuturePointing d := ⟨⟨timeVec, by
rw [NormOneLorentzVector.mem_iff, on_timeVec]⟩, by
rw [mem_iff, timeVec_time]; exact Real.zero_lt_one⟩
/-- A continuous path from `timeVecNormOneFuture` to any other. -/
noncomputable def pathFromTime (u : FuturePointing d) : Path timeVecNormOneFuture u where
toFun t := ⟨
@ -266,9 +262,6 @@ noncomputable def pathFromTime (u : FuturePointing d) : Path timeVecNormOneFutur
simp only [Set.Icc.coe_one, one_pow, space, one_mul, Fin.isValue]
exact rfl
lemma isPathConnected : IsPathConnected (@Set.univ (FuturePointing d)) := by
use timeVecNormOneFuture
apply And.intro trivial ?_
@ -276,7 +269,6 @@ lemma isPathConnected : IsPathConnected (@Set.univ (FuturePointing d)) := by
use pathFromTime y
exact fun _ => a
lemma metric_continuous (u : LorentzVector d) :
Continuous (fun (a : FuturePointing d) => ⟪u, a.1.1⟫ₘ) := by
simp only [minkowskiMetric.eq_time_minus_inner_prod]
@ -289,8 +281,6 @@ lemma metric_continuous (u : LorentzVector d) :
(Continuous.comp' (Pi.continuous_precomp Sum.inr) (Continuous.comp'
continuous_subtype_val continuous_subtype_val))
end FuturePointing
end NormOneLorentzVector