reactor: Removal of double spaces
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jstoobysmith
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ce92e1d649
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64 changed files with 550 additions and 546 deletions
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@ -34,7 +34,7 @@ open BigOperators
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variable {n : ℕ}
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open VectorLikeEvenPlane
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/-- A property on `LinSols`, satisfied if every point on the line between the two planes
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/-- A property on `LinSols`, satisfied if every point on the line between the two planes
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in the basis through that point is in the cubic. -/
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def LineInCubic (S : (PureU1 (2 * n.succ)).LinSols) : Prop :=
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∀ (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (_ : S.val = Pa g f) (a b : ℚ) ,
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@ -61,18 +61,18 @@ lemma lineInCubic_expand {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic S)
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then `accCubeTriLinSymm.toFun (P g, P g, P! f) = 0`.
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-/
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lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic S) :
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∀ (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
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∀ (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
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accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
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intro g f hS
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linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1) -
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(lineInCubic_expand h g f hS 1 2) / 6
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/-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
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/-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
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def LineInCubicPerm (S : (PureU1 (2 * n.succ)).LinSols) : Prop :=
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∀ (M : (FamilyPermutations (2 * n.succ)).group ),
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LineInCubic ((FamilyPermutations (2 * n.succ)).linSolRep M S)
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/-- If `lineInCubicPerm S` then `lineInCubic S`. -/
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/-- If `lineInCubicPerm S` then `lineInCubic S`. -/
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lemma lineInCubicPerm_self {S : (PureU1 (2 * n.succ)).LinSols}
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(hS : LineInCubicPerm S) : LineInCubic S := hS 1
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@ -94,7 +94,7 @@ lemma lineInCubicPerm_swap {S : (PureU1 (2 * n.succ)).LinSols}
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(S.val (δ!₂ j) - S.val (δ!₁ j))
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* accCubeTriLinSymm (P g) (P g) (basis!AsCharges j) = 0 := by
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intro j g f h
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let S' := (FamilyPermutations (2 * n.succ)).linSolRep (pairSwap (δ!₁ j) (δ!₂ j)) S
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let S' := (FamilyPermutations (2 * n.succ)).linSolRep (pairSwap (δ!₁ j) (δ!₂ j)) S
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have hSS' : ((FamilyPermutations (2 * n.succ)).linSolRep (pairSwap (δ!₁ j) (δ!₂ j))) S = S' := rfl
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obtain ⟨g', f', hall⟩ := span_basis_swap! j hSS' g f h
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have h1 := line_in_cubic_P_P_P! (lineInCubicPerm_self LIC) g f h
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@ -106,21 +106,21 @@ lemma lineInCubicPerm_swap {S : (PureU1 (2 * n.succ)).LinSols}
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lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ )).LinSols}
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(f : Fin n.succ.succ → ℚ) (g : Fin n.succ → ℚ) (hS : S.val = Pa f g) :
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accCubeTriLinSymm (P f) (P f) (basis!AsCharges (Fin.last n)) =
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accCubeTriLinSymm (P f) (P f) (basis!AsCharges (Fin.last n)) =
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- (S.val (δ!₂ (Fin.last n)) + S.val (δ!₁ (Fin.last n))) * (2 * S.val δ!₄ +
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S.val (δ!₂ (Fin.last n)) + S.val (δ!₁ (Fin.last n))) := by
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rw [P_P_P!_accCube f (Fin.last n)]
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S.val (δ!₂ (Fin.last n)) + S.val (δ!₁ (Fin.last n))) := by
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rw [P_P_P!_accCube f (Fin.last n)]
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have h1 := Pa_δ!₄ f g
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have h2 := Pa_δ!₁ f g (Fin.last n)
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have h3 := Pa_δ!₂ f g (Fin.last n)
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simp at h1 h2 h3
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have hl : f (Fin.succ (Fin.last (n ))) = - Pa f g δ!₄ := by
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have hl : f (Fin.succ (Fin.last (n ))) = - Pa f g δ!₄ := by
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simp_all only [Fin.succ_last, neg_neg]
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erw [hl] at h2
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have hg : g (Fin.last n) = Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄ := by
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have hg : g (Fin.last n) = Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄ := by
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linear_combination -(1 * h2)
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have hll : f (Fin.castSucc (Fin.last (n ))) =
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- (Pa f g (δ!₂ (Fin.last n)) + Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄) := by
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have hll : f (Fin.castSucc (Fin.last (n ))) =
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- (Pa f g (δ!₂ (Fin.last n)) + Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄) := by
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linear_combination h3 - 1 * hg
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rw [← hS] at hl hll
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rw [hl, hll]
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@ -145,7 +145,7 @@ lemma lineInCubicPerm_last_cond {S : (PureU1 (2 * n.succ.succ)).LinSols}
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apply Or.inr
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exact h1
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lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ)).LinSols}
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lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ)).LinSols}
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(LIC : LineInCubicPerm S) : LineInPlaneCond S := by
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refine @Prop_three (2 * n.succ.succ) LineInPlaneProp S (δ!₂ (Fin.last n)) (δ!₁ (Fin.last n))
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δ!₄ ?_ ?_ ?_ ?_
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@ -156,15 +156,15 @@ lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ)).LinSols}
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intro M
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exact lineInCubicPerm_last_cond (lineInCubicPerm_permute LIC M)
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lemma lineInCubicPerm_constAbs {S : (PureU1 (2 * n.succ.succ)).Sols}
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lemma lineInCubicPerm_constAbs {S : (PureU1 (2 * n.succ.succ)).Sols}
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(LIC : LineInCubicPerm S.1.1) : ConstAbs S.val :=
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linesInPlane_constAbs_AF S (lineInCubicPerm_last_perm LIC)
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theorem lineInCubicPerm_vectorLike {S : (PureU1 (2 * n.succ.succ)).Sols}
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theorem lineInCubicPerm_vectorLike {S : (PureU1 (2 * n.succ.succ)).Sols}
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(LIC : LineInCubicPerm S.1.1) : VectorLikeEven S.val :=
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ConstAbs.boundary_value_even S.1.1 (lineInCubicPerm_constAbs LIC)
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theorem lineInCubicPerm_in_plane (S : (PureU1 (2 * n.succ.succ)).Sols)
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theorem lineInCubicPerm_in_plane (S : (PureU1 (2 * n.succ.succ)).Sols)
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(LIC : LineInCubicPerm S.1.1) : ∃ (M : (FamilyPermutations (2 * n.succ.succ)).group),
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(FamilyPermutations (2 * n.succ.succ)).linSolRep M S.1.1
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∈ Submodule.span ℚ (Set.range basis) :=
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