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refactor: Last batch of multi-goal proofs

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jstoobysmith 2024-08-21 06:40:58 -04:00
parent b9479c904d
commit c0499483a8
43 changed files with 910 additions and 955 deletions
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32
HepLean/Mathematics/SO3/Basic.lean
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@ -176,22 +176,22 @@ lemma exists_stationary_vec (A : SO(3)) :
have hvn : ‖v‖ ≠ 0 := norm_ne_zero_iff.mpr hv.2
use (1/‖v‖) • v
apply And.intro
rw [@orthonormal_iff_ite]
intro v1 v2
have hv1 := v1.2
have hv2 := v2.2
simp_all only [one_div, Set.mem_singleton_iff]
have hveq : v1 = v2 := by
rw [@Subtype.ext_iff]
simp_all only
subst hveq
simp only [Set.restrict_apply, PiLp.smul_apply, smul_eq_mul,
_root_.map_mul, map_inv₀, conj_trivial, ↓reduceIte]
rw [inner_smul_right, inner_smul_left, real_inner_self_eq_norm_sq v]
field_simp
ring
rw [_root_.map_smul, End.mem_eigenspace_iff.mp hv.1]
simp
· rw [@orthonormal_iff_ite]
intro v1 v2
have hv1 := v1.2
have hv2 := v2.2
simp_all only [one_div, Set.mem_singleton_iff]
have hveq : v1 = v2 := by
rw [@Subtype.ext_iff]
simp_all only
subst hveq
simp only [Set.restrict_apply, PiLp.smul_apply, smul_eq_mul,
_root_.map_mul, map_inv₀, conj_trivial, ↓reduceIte]
rw [inner_smul_right, inner_smul_left, real_inner_self_eq_norm_sq v]
field_simp
ring
· rw [_root_.map_smul, End.mem_eigenspace_iff.mp hv.1]
simp
lemma exists_basis_preserved (A : SO(3)) :
∃ (b : OrthonormalBasis (Fin 3) ℝ (EuclideanSpace ℝ (Fin 3))), A.toEnd (b 0) = b 0 := by