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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/Mathematics/SO3/Basic.lean
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@ -59,7 +59,7 @@ def toGL : SO(3) →* GL (Fin 3) ℝ where
map_one' := by
simp
rfl
map_mul' x y := by
map_mul' x y := by
simp only [_root_.mul_inv_rev, coe_inv]
ext
rfl
@ -143,16 +143,16 @@ instance : TopologicalGroup SO(3) :=
Inducing.topologicalGroup toGL toGL_embedding.toInducing
lemma det_minus_id (A : SO(3)) : det (A.1 - 1) = 0 := by
have h1 : det (A.1 - 1) = - det (A.1 - 1) :=
have h1 : det (A.1 - 1) = - det (A.1 - 1) :=
calc
det (A.1 - 1) = det (A.1 - A.1 * A.1ᵀ) := by simp [A.2.2]
_ = det A.1 * det (1 - A.1ᵀ) := by rw [← det_mul, mul_sub, mul_one]
_ = det A.1 * det (1 - A.1ᵀ) := by rw [← det_mul, mul_sub, mul_one]
_ = det (1 - A.1ᵀ):= by simp [A.2.1]
_ = det (1 - A.1ᵀ)ᵀ := by rw [det_transpose]
_ = det (1 - A.1) := by simp
_ = det (- (A.1 - 1)) := by simp
_ = (- 1) ^ 3 * det (A.1 - 1) := by simp only [det_neg, Fintype.card_fin, neg_mul, one_mul]
_ = - det (A.1 - 1) := by simp [pow_three]
_ = (- 1) ^ 3 * det (A.1 - 1) := by simp only [det_neg, Fintype.card_fin, neg_mul, one_mul]
_ = - det (A.1 - 1) := by simp [pow_three]
simpa using h1
@[simp]
@ -161,7 +161,7 @@ lemma det_id_minus (A : SO(3)) : det (1 - A.1) = 0 := by
calc
det (1 - A.1) = det (- (A.1 - 1)) := by simp
_ = (- 1) ^ 3 * det (A.1 - 1) := by simp only [det_neg, Fintype.card_fin, neg_mul, one_mul]
_ = - det (A.1 - 1) := by simp [pow_three]
_ = - det (A.1 - 1) := by simp [pow_three]
rw [h1, det_minus_id]
simp only [neg_zero]
@ -216,7 +216,7 @@ lemma exists_basis_preserved (A : SO(3)) :
obtain ⟨v, hv⟩ := exists_stationary_vec A
have h3 : FiniteDimensional.finrank ℝ (EuclideanSpace ℝ (Fin 3)) = Fintype.card (Fin 3) := by
simp_all only [toEnd_apply, finrank_euclideanSpace, Fintype.card_fin]
obtain ⟨b, hb⟩ := Orthonormal.exists_orthonormalBasis_extension_of_card_eq h3 hv.1
obtain ⟨b, hb⟩ := Orthonormal.exists_orthonormalBasis_extension_of_card_eq h3 hv.1
simp at hb
use b
rw [hb, hv.2]