feat: Add basics for SMNu PlusU1
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jstoobysmith
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4 changed files with 207 additions and 3 deletions
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@ -8,8 +8,7 @@ import HepLean.AnomalyCancellation.SMNu.Permutations
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/-!
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# ACC system for SM with RHN (without hypercharge).
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We define the ACC system for the Standard Model with right-handed neutrinos and no gravitational
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anomaly.
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We define the ACC system for the Standard Model (without hypercharge) with right-handed neutrinos.
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-/
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141
HepLean/AnomalyCancellation/SMNu/PlusU1/Basic.lean
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141
HepLean/AnomalyCancellation/SMNu/PlusU1/Basic.lean
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@ -0,0 +1,141 @@
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.AnomalyCancellation.SMNu.Basic
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import HepLean.AnomalyCancellation.SMNu.Permutations
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/-!
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# ACC system for SM with RHN
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We define the ACC system for the Standard Model with right-handed neutrinos.
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-/
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universe v u
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namespace SMRHN
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open SMνCharges
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open SMνACCs
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open BigOperators
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/-- The ACC system for the SM plus RHN with an additional U1. -/
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@[simps!]
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def PlusU1 (n : ℕ) : ACCSystem where
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numberLinear := 4
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linearACCs := fun i =>
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match i with
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| 0 => @accGrav n
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| 1 => accSU2
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| 2 => accSU3
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| 3 => accYY
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numberQuadratic := 1
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quadraticACCs := fun i =>
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match i with
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| 0 => accQuad
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cubicACC := accCube
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namespace PlusU1
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variable {n : ℕ}
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lemma gravSol (S : (PlusU1 n).LinSols) : accGrav S.val = 0 := by
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have hS := S.linearSol
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simp at hS
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exact hS 0
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lemma SU2Sol (S : (PlusU1 n).LinSols) : accSU2 S.val = 0 := by
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have hS := S.linearSol
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simp at hS
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exact hS 1
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lemma SU3Sol (S : (PlusU1 n).LinSols) : accSU3 S.val = 0 := by
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have hS := S.linearSol
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simp at hS
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exact hS 2
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lemma YYsol (S : (PlusU1 n).LinSols) : accYY S.val = 0 := by
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have hS := S.linearSol
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simp at hS
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exact hS 3
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lemma quadSol (S : (PlusU1 n).QuadSols) : accQuad S.val = 0 := by
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have hS := S.quadSol
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simp at hS
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exact hS 0
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lemma cubeSol (S : (PlusU1 n).Sols) : accCube S.val = 0 := by
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exact S.cubicSol
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/-- An element of `charges` which satisfies the linear ACCs
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gives us a element of `LinSols`. -/
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def chargeToLinear (S : (PlusU1 n).charges) (hGrav : accGrav S = 0)
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(hSU2 : accSU2 S = 0) (hSU3 : accSU3 S = 0) (hYY : accYY S = 0) :
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(PlusU1 n).LinSols :=
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⟨S, by
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intro i
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simp at i
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match i with
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| 0 => exact hGrav
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| 1 => exact hSU2
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| 2 => exact hSU3
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| 3 => exact hYY⟩
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/-- An element of `LinSols` which satisfies the quadratic ACCs
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gives us a element of `AnomalyFreeQuad`. -/
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def linearToQuad (S : (PlusU1 n).LinSols) (hQ : accQuad S.val = 0) :
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(PlusU1 n).QuadSols :=
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⟨S, by
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intro i
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simp at i
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match i with
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| 0 => exact hQ⟩
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/-- An element of `QuadSols` which satisfies the quadratic ACCs
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gives us a element of `Sols`. -/
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def quadToAF (S : (PlusU1 n).QuadSols) (hc : accCube S.val = 0) :
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(PlusU1 n).Sols := ⟨S, hc⟩
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/-- An element of `charges` which satisfies the linear and quadratic ACCs
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gives us a element of `QuadSols`. -/
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def chargeToQuad (S : (PlusU1 n).charges) (hGrav : accGrav S = 0)
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(hSU2 : accSU2 S = 0) (hSU3 : accSU3 S = 0) (hYY : accYY S = 0) (hQ : accQuad S = 0) :
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(PlusU1 n).QuadSols :=
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linearToQuad (chargeToLinear S hGrav hSU2 hSU3 hYY) hQ
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/-- An element of `charges` which satisfies the linear, quadratic and cubic ACCs
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gives us a element of `Sols`. -/
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def chargeToAF (S : (PlusU1 n).charges) (hGrav : accGrav S = 0) (hSU2 : accSU2 S = 0)
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(hSU3 : accSU3 S = 0) (hYY : accYY S = 0) (hQ : accQuad S = 0) (hc : accCube S = 0) :
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(PlusU1 n).Sols :=
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quadToAF (chargeToQuad S hGrav hSU2 hSU3 hYY hQ) hc
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/-- An element of `LinSols` which satisfies the quadratic and cubic ACCs
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gives us a element of `Sols`. -/
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def linearToAF (S : (PlusU1 n).LinSols) (hQ : accQuad S.val = 0)
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(hc : accCube S.val = 0) : (PlusU1 n).Sols :=
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quadToAF (linearToQuad S hQ) hc
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/-- The permutations acting on the ACC system corresponding to the SM with RHN. -/
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def perm (n : ℕ) : ACCSystemGroupAction (PlusU1 n) where
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group := permGroup n
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groupInst := inferInstance
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rep := repCharges
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linearInvariant := by
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intro i
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simp at i
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match i with
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| 0 => exact accGrav_invariant
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| 1 => exact accSU2_invariant
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| 2 => exact accSU3_invariant
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| 3 => exact accYY_invariant
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quadInvariant := by
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intro i
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simp at i
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match i with
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| 0 => exact accQuad_invariant
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cubicInvariant := accCube_invariant
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end PlusU1
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end SMRHN
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62
HepLean/AnomalyCancellation/SMNu/PlusU1/FamilyMaps.lean
Normal file
62
HepLean/AnomalyCancellation/SMNu/PlusU1/FamilyMaps.lean
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@ -0,0 +1,62 @@
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.AnomalyCancellation.SMNu.PlusU1.Basic
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import HepLean.AnomalyCancellation.SMNu.FamilyMaps
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/-!
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# Family Maps for SM with RHN
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We give some propererties of the family maps for the SM with RHN, in particular, we
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define family universal maps in the case of `LinSols`, `QuadSols`, and `Sols`.
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-/
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universe v u
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namespace SMRHN
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namespace PlusU1
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open SMνCharges
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open SMνACCs
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open BigOperators
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variable {n : ℕ}
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/-- The family universal maps on `LinSols`. -/
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def familyUniversalLinear (n : ℕ) :
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(PlusU1 1).LinSols →ₗ[ℚ] (PlusU1 n).LinSols where
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toFun S := chargeToLinear (familyUniversal n S.val)
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(by rw [familyUniversal_accGrav, gravSol S, mul_zero])
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(by rw [familyUniversal_accSU2, SU2Sol S, mul_zero])
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(by rw [familyUniversal_accSU3, SU3Sol S, mul_zero])
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(by rw [familyUniversal_accYY, YYsol S, mul_zero])
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map_add' S T := by
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apply ACCSystemLinear.LinSols.ext
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exact (familyUniversal n).map_add' _ _
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map_smul' a S := by
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apply ACCSystemLinear.LinSols.ext
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exact (familyUniversal n).map_smul' _ _
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/-- The family universal maps on `QuadSols`. -/
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def familyUniversalQuad (n : ℕ) :
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(PlusU1 1).QuadSols → (PlusU1 n).QuadSols := fun S =>
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chargeToQuad (familyUniversal n S.val)
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(by rw [familyUniversal_accGrav, gravSol S.1, mul_zero])
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(by rw [familyUniversal_accSU2, SU2Sol S.1, mul_zero])
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(by rw [familyUniversal_accSU3, SU3Sol S.1, mul_zero])
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(by rw [familyUniversal_accYY, YYsol S.1, mul_zero])
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(by rw [familyUniversal_accQuad, quadSol S, mul_zero])
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/-- The family universal maps on `Sols`. -/
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def familyUniversalAF (n : ℕ) :
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(PlusU1 1).Sols → (PlusU1 n).Sols := fun S =>
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chargeToAF (familyUniversal n S.val)
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(by rw [familyUniversal_accGrav, gravSol S.1.1, mul_zero])
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(by rw [familyUniversal_accSU2, SU2Sol S.1.1, mul_zero])
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(by rw [familyUniversal_accSU3, SU3Sol S.1.1, mul_zero])
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(by rw [familyUniversal_accYY, YYsol S.1.1, mul_zero])
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(by rw [familyUniversal_accQuad, quadSol S.1, mul_zero])
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(by rw [familyUniversal_accCube, cubeSol S, mul_zero])
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end PlusU1
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end SMRHN
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