refactor: Lint
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4 changed files with 39 additions and 31 deletions
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@ -51,7 +51,7 @@ lemma charges_eq_toSpecies_eq (S T : (SMCharges n).charges) :
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apply Iff.intro
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intro h
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rw [h]
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simp
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simp only [forall_const]
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intro h
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apply toSpeciesEquiv.injective
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funext i
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@ -108,7 +108,8 @@ def accGrav : (SMCharges n).charges →ₗ[ℚ] ℚ where
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lemma accGrav_ext {S T : (SMCharges n).charges}
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(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
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accGrav S = accGrav T := by
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simp
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simp only [accGrav, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
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AddHom.coe_mk]
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repeat erw [Finset.sum_add_distrib]
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repeat erw [← Finset.mul_sum]
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repeat erw [hj]
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@ -137,7 +138,8 @@ def accSU2 : (SMCharges n).charges →ₗ[ℚ] ℚ where
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lemma accSU2_ext {S T : (SMCharges n).charges}
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(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
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accSU2 S = accSU2 T := by
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simp
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simp only [accSU2, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
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AddHom.coe_mk]
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repeat erw [Finset.sum_add_distrib]
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repeat erw [← Finset.mul_sum]
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repeat erw [hj]
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@ -166,7 +168,8 @@ def accSU3 : (SMCharges n).charges →ₗ[ℚ] ℚ where
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lemma accSU3_ext {S T : (SMCharges n).charges}
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(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
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accSU3 S = accSU3 T := by
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simp
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simp only [accSU3, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
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AddHom.coe_mk]
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repeat erw [Finset.sum_add_distrib]
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repeat erw [← Finset.mul_sum]
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repeat erw [hj]
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@ -196,7 +199,8 @@ def accYY : (SMCharges n).charges →ₗ[ℚ] ℚ where
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lemma accYY_ext {S T : (SMCharges n).charges}
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(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
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accYY S = accYY T := by
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simp
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simp only [accYY, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
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AddHom.coe_mk]
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repeat erw [Finset.sum_add_distrib]
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repeat erw [← Finset.mul_sum]
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repeat erw [hj]
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@ -224,10 +228,11 @@ def quadBiLin : BiLinearSymm (SMCharges n).charges where
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apply Fintype.sum_congr
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intro i
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repeat erw [map_add]
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simp
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simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue, neg_mul,
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one_mul]
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ring
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swap' S T := by
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simp
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simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, neg_mul, one_mul]
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apply Fintype.sum_congr
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intro i
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ring
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@ -274,15 +279,15 @@ def cubeTriLin : TriLinearSymm (SMCharges n).charges where
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apply Fintype.sum_congr
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intro i
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repeat erw [map_add]
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simp
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simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue]
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ring
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swap₁' S T L := by
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simp
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simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
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apply Fintype.sum_congr
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intro i
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ring
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swap₂' S T L := by
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simp
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simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
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apply Fintype.sum_congr
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intro i
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ring
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@ -66,7 +66,7 @@ def speciesEmbed (m n : ℕ) :
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0
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map_add' S T := by
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funext i
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simp
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simp only [SMSpecies_numberCharges, ACCSystemCharges.chargesAddCommMonoid_add]
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by_cases hi : i.val < m
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erw [dif_pos hi, dif_pos hi, dif_pos hi]
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erw [dif_neg hi, dif_neg hi, dif_neg hi]
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@ -6,7 +6,6 @@ Authors: Joseph Tooby-Smith
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import HepLean.AnomalyCancellation.SM.Basic
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import HepLean.AnomalyCancellation.SM.NoGrav.Basic
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import HepLean.AnomalyCancellation.SM.NoGrav.One.LinearParameterization
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universe v u
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/-!
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# Lemmas for 1 family SM Accs
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@ -16,6 +15,7 @@ https://arxiv.org/abs/1907.00514
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That eveery solution to the ACCs without gravity satifies for free the gravitational anomaly.
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-/
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universe v u
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namespace SM
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namespace SMNoGrav
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namespace One
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@ -9,8 +9,6 @@ import Mathlib.Tactic.FieldSimp
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import Mathlib.Tactic.Linarith
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import Mathlib.NumberTheory.FLT.Basic
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import Mathlib.Algebra.QuadraticDiscriminant
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universe v u
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/-!
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# Parameterizations for solutions to the linear ACCs for 1 family
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@ -22,7 +20,7 @@ These parameterizations are based on:
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https://arxiv.org/abs/1907.00514
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-/
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universe v u
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namespace SM
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namespace SMNoGrav
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namespace One
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@ -43,7 +41,8 @@ structure linearParameters where
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namespace linearParameters
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@[ext]
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lemma ext {S T : linearParameters} (hQ : S.Q' = T.Q') (hY : S.Y = T.Y) (hE : S.E' = T.E') : S = T := by
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lemma ext {S T : linearParameters} (hQ : S.Q' = T.Q') (hY : S.Y = T.Y) (hE : S.E' = T.E') :
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S = T := by
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cases' S
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simp_all only
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@ -57,7 +56,8 @@ def asCharges (S : linearParameters) : (SMNoGrav 1).charges := fun i =>
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| (3: Fin 5) => - 3 * S.Q'
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| (4 : Fin 5) => S.E'
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lemma speciesVal (S : linearParameters) : (toSpecies i) S.asCharges (0 : Fin 1) = S.asCharges i := by
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lemma speciesVal (S : linearParameters) :
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(toSpecies i) S.asCharges (0 : Fin 1) = S.asCharges i := by
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match i with
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| 0 => rfl
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| 1 => rfl
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@ -76,7 +76,7 @@ def asLinear (S : linearParameters) : (SMNoGrav 1).LinSols :=
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simp only [accSU3, SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero,
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Fin.isValue, Finset.sum_singleton, LinearMap.coe_mk, AddHom.coe_mk]
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repeat erw [speciesVal]
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simp
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simp only [asCharges, neg_add_rev]
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ring)
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lemma asLinear_val (S : linearParameters) : S.asLinear.val = S.asCharges := by
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@ -92,7 +92,7 @@ lemma cubic (S : linearParameters) :
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simp only [SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
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Finset.sum_singleton]
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repeat erw [speciesVal]
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simp
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simp only [asCharges, neg_add_rev, neg_mul, mul_neg, neg_neg]
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ring
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lemma cubic_zero_Q'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
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@ -129,13 +129,13 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
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repeat erw [speciesVal]
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simp only [Fin.isValue]
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repeat erw [speciesVal]
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simp
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simp only [asCharges, neg_add_rev]
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ring
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simp only [toSpecies_apply]
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repeat erw [speciesVal]
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rfl
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right_inv S := by
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simp
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simp only [Fin.isValue, toSpecies_apply]
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apply ACCSystemLinear.LinSols.ext
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rw [charges_eq_toSpecies_eq]
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intro i
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@ -167,7 +167,7 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
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/-- The bijection between the linear parameters and `(SMNoGrav 1).LinSols` in the special
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case when Q and E are both not zero. -/
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def bijectionQEZero : {S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0} ≃
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{S : (SMNoGrav 1).LinSols // Q S.val (0 : Fin 1) ≠ 0 ∧ E S.val (0 : Fin 1) ≠ 0} where
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{S : (SMNoGrav 1).LinSols // Q S.val (0 : Fin 1) ≠ 0 ∧ E S.val (0 : Fin 1) ≠ 0} where
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toFun S := ⟨bijection S, S.2⟩
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invFun S := ⟨bijection.symm S, S.2⟩
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left_inv S := by
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@ -183,7 +183,7 @@ lemma grav (S : linearParameters) :
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simp only [SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
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Finset.sum_singleton, LinearMap.coe_mk, AddHom.coe_mk]
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repeat erw [speciesVal]
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simp
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simp only [asCharges, neg_add_rev, neg_mul, mul_neg]
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ring_nf
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rw [add_comm, add_eq_zero_iff_eq_neg]
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simp
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@ -217,7 +217,8 @@ def toLinearParameters (S : linearParametersQENeqZero) :
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⟨⟨S.x, 3 * S.x * (S.v - S.w) / (S.v + S.w), - 6 * S.x / (S.v + S.w)⟩,
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by
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apply And.intro S.hx
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simp
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simp only [neg_mul, ne_eq, div_eq_zero_iff, neg_eq_zero, mul_eq_zero, OfNat.ofNat_ne_zero,
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false_or]
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rw [not_or]
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exact And.intro S.hx S.hvw⟩
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@ -228,11 +229,11 @@ def tolinearParametersQNeqZero (S : {S : linearParameters // S.Q' ≠ 0 ∧ S.
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linearParametersQENeqZero :=
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⟨S.1.Q', - (3 * S.1.Q' + S.1.Y) / S.1.E', - (3 * S.1.Q' - S.1.Y)/ S.1.E', S.2.1,
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by
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simp
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simp only [ne_eq, neg_add_rev, neg_sub]
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field_simp
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rw [not_or]
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ring_nf
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simp
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simp only [neg_eq_zero, mul_eq_zero, OfNat.ofNat_ne_zero, or_false]
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exact S.2⟩
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/-- A bijection between the type `linearParametersQENeqZero` and linear parameters
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@ -246,10 +247,11 @@ def bijectionLinearParameters :
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have hvw := S.hvw
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have hQ := S.hx
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apply linearParametersQENeqZero.ext
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simp
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simp only [tolinearParametersQNeqZero_x, toLinearParameters_coe_Q']
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field_simp
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ring
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simp
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simp only [tolinearParametersQNeqZero_w, toLinearParameters_coe_Y, toLinearParameters_coe_Q',
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toLinearParameters_coe_E']
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field_simp
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ring
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right_inv S := by
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@ -257,7 +259,7 @@ def bijectionLinearParameters :
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have hQ := S.2.1
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have hE := S.2.2
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apply linearParameters.ext
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simp
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simp only [ne_eq, toLinearParameters_coe_Q', tolinearParametersQNeqZero_x]
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field_simp
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ring_nf
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field_simp [hQ, hE]
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@ -275,7 +277,8 @@ def bijection : linearParametersQENeqZero ≃
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lemma cubic (S : linearParametersQENeqZero) :
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accCube (bijection S).1.val = 0 ↔ S.v ^ 3 + S.w ^ 3 = -1 := by
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erw [linearParameters.cubic]
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simp
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simp only [ne_eq, bijectionLinearParameters_apply_coe_Q', neg_mul,
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bijectionLinearParameters_apply_coe_Y, div_pow, bijectionLinearParameters_apply_coe_E']
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have hvw := S.hvw
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have hQ := S.hx
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field_simp
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@ -365,7 +368,7 @@ lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1
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have h' := cube_w_v S h
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cases' h' with h h
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rw [h.1, h.2]
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simp
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simp only [add_zero]
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rw [h.1, h.2]
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simp
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