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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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14
HepLean/SpaceTime/LorentzVector/NormOne.lean
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@ -36,7 +36,7 @@ def neg : NormOneLorentzVector d := ⟨- v, by
simp only [map_neg, LinearMap.neg_apply, neg_neg]
exact v.2⟩
lemma time_sq : v.1.time ^ 2 = 1 + ‖v.1.space‖ ^ 2 := by
lemma time_sq : v.1.time ^ 2 = 1 + ‖v.1.space‖ ^ 2 := by
rw [time_sq_eq_metric_add_space, v.2]
lemma abs_time_ge_one : 1 ≤ |v.1.time| := by
@ -48,7 +48,7 @@ lemma norm_space_le_abs_time : ‖v.1.space‖ < |v.1.time| := by
rw [(abs_norm _).symm, ← @sq_lt_sq, time_sq]
exact lt_one_add (‖(v.1).space‖ ^ 2)
lemma norm_space_leq_abs_time : ‖v.1.space‖ ≤ |v.1.time| :=
lemma norm_space_leq_abs_time : ‖v.1.space‖ ≤ |v.1.time| :=
le_of_lt (norm_space_le_abs_time v)
lemma time_le_minus_one_or_ge_one : v.1.time ≤ -1 ∨ 1 ≤ v.1.time :=
@ -77,7 +77,7 @@ lemma time_pos_iff : 0 < v.1.time ↔ 1 ≤ v.1.time := by
· exact (time_nonneg_iff v).mp (le_of_lt h)
· linarith
lemma time_abs_sub_space_norm :
lemma time_abs_sub_space_norm :
0 ≤ |v.1.time| * |w.1.time| - ‖v.1.space‖ * ‖w.1.space‖ := by
apply sub_nonneg.mpr
apply mul_le_mul (norm_space_leq_abs_time v) (norm_space_leq_abs_time w) ?_ ?_
@ -167,7 +167,7 @@ lemma metric_reflect_mem_mem (h : v ∈ FuturePointing d) (hw : w ∈ FuturePoin
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
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]
@ -179,10 +179,10 @@ lemma metric_reflect_mem_not_mem (h : v ∈ FuturePointing d) (hw : w ∉ Future
apply le_of_le_of_eq h1 ?_
simp [neg]
lemma metric_reflect_not_mem_mem (h : v ∉ FuturePointing d) (hw : w ∈ FuturePointing d) :
lemma metric_reflect_not_mem_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]
have h1 := metric_reflect_mem_mem ((not_mem_iff_neg v).mp h) hw
have h1 := metric_reflect_mem_mem ((not_mem_iff_neg v).mp h) hw
apply le_of_le_of_eq h1 ?_
simp [neg]
@ -264,7 +264,7 @@ noncomputable def pathFromTime (u : FuturePointing d) : Path timeVecNormOneFutur
lemma isPathConnected : IsPathConnected (@Set.univ (FuturePointing d)) := by
use timeVecNormOneFuture
apply And.intro trivial ?_
apply And.intro trivial ?_
intro y a
use pathFromTime y
exact fun _ => a