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refactor: Lint

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jstoobysmith 2024-11-11 07:22:36 +00:00
parent a8243f4e79
commit 081955c993
6 changed files with 35 additions and 34 deletions
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14
HepLean/Lorentz/RealVector/NormOne.lean
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@ -22,7 +22,7 @@ variable {d : ℕ}
/-- The set of Lorentz vectors with norm 1. -/
def NormOne (d : ℕ) : Set (Contr d) := fun v => ⟪v, v⟫ₘ = (1 : ℝ)
noncomputable section
noncomputable section
namespace NormOne
@ -68,7 +68,7 @@ lemma _root_.LorentzGroup.inl_inl_mul (Λ Λ' : LorentzGroup d) : (Λ * Λ').1 (
⟪(LorentzGroup.toNormOne (LorentzGroup.transpose Λ)).1,
(Contr d).ρ LorentzGroup.parity (LorentzGroup.toNormOne Λ').1⟫ₘ := by
rw [contrContrContractField.right_parity]
simp only [Fin.isValue, lorentzGroupIsGroup_mul_coe, Matrix.mul_apply, Fintype.sum_sum_type,
simp only [Fin.isValue, lorentzGroupIsGroup_mul_coe, Matrix.mul_apply, Fintype.sum_sum_type,
Finset.univ_unique, Fin.default_eq_zero, Finset.sum_singleton,
LorentzGroup.transpose, PiLp.inner_apply, Function.comp_apply,
RCLike.inner_apply, conj_trivial]
@ -80,7 +80,7 @@ lemma _root_.LorentzGroup.inl_inl_mul (Λ Λ' : LorentzGroup d) : (Λ * Λ').1 (
rw [LorentzGroup.toNormOne_inr, LorentzGroup.toNormOne_inr]
rfl
lemma inl_sq : v.val.val (Sum.inl 0) ^ 2 = 1 + ‖ContrMod.toSpace v.val‖ ^ 2 := by
lemma inl_sq : v.val.val (Sum.inl 0) ^ 2 = 1 + ‖ContrMod.toSpace v.val‖ ^ 2 := by
rw [contrContrContractField.inl_sq_eq, v.2]
congr
rw [← real_inner_self_eq_norm_sq]
@ -99,14 +99,14 @@ lemma inl_le_neg_one_or_one_le_inl : v.val.val (Sum.inl 0) ≤ -1 ∨ 1 ≤ v.va
lemma norm_space_le_abs_inl : ‖v.1.toSpace‖ < |v.val.val (Sum.inl 0)| := by
rw [(abs_norm _).symm, ← @sq_lt_sq, inl_sq]
change ‖ContrMod.toSpace v.val‖ ^ 2 < 1 + ‖ContrMod.toSpace v.val‖ ^ 2
change ‖ContrMod.toSpace v.val‖ ^ 2 < 1 + ‖ContrMod.toSpace v.val‖ ^ 2
exact lt_one_add (‖(v.1).toSpace‖ ^ 2)
lemma norm_space_leq_abs_inl : ‖v.1.toSpace‖ ≤ |v.val.val (Sum.inl 0)| :=
le_of_lt (norm_space_le_abs_inl v)
lemma inl_abs_sub_space_norm :
0 ≤ |v.val.val (Sum.inl 0)| * |w.val.val (Sum.inl 0)| - ‖v.1.toSpace‖ * ‖w.1.toSpace‖ := by
0 ≤ |v.val.val (Sum.inl 0)| * |w.val.val (Sum.inl 0)| - ‖v.1.toSpace‖ * ‖w.1.toSpace‖ := by
apply sub_nonneg.mpr
apply mul_le_mul (norm_space_leq_abs_inl v) (norm_space_leq_abs_inl w) ?_ ?_
· exact norm_nonneg _
@ -148,7 +148,6 @@ lemma mem_iff_parity_mem : v ∈ FuturePointing d ↔ ⟨(Contr d).ρ LorentzGro
change _ ↔ 0 < (minkowskiMatrix.mulVec v.val.val) (Sum.inl 0)
simp only [Fin.isValue, minkowskiMatrix.mulVec_inl_0]
lemma not_mem_iff_inl_le_zero : v ∉ FuturePointing d ↔ v.val.val (Sum.inl 0) ≤ 0 := by
rw [mem_iff]
simp
@ -173,7 +172,7 @@ lemma not_mem_iff_neg : v ∉ FuturePointing d ↔ neg v ∈ FuturePointing d :=
variable (f f' : FuturePointing d)
lemma inl_nonneg : 0 ≤ f.val.val.val (Sum.inl 0):= le_of_lt f.2
lemma inl_nonneg : 0 ≤ f.val.val.val (Sum.inl 0) := le_of_lt f.2
lemma abs_inl : |f.val.val.val (Sum.inl 0)| = f.val.val.val (Sum.inl 0) :=
abs_of_nonneg (inl_nonneg f)
@ -231,7 +230,6 @@ namespace FuturePointing
## Topology
-/
/-- The `FuturePointing d` which has all space components zero. -/
@[simps!]
noncomputable def timeVecNormOneFuture : FuturePointing d := ⟨⟨ContrMod.stdBasis (Sum.inl 0), by