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reactor: Removal of double spaces

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jstoobysmith 2024-07-12 11:23:02 -04:00
parent ce92e1d649
commit 13f62a50eb
64 changed files with 550 additions and 546 deletions
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22
HepLean/AnomalyCancellation/PureU1/Odd/LineInCubic.lean
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@ -34,10 +34,10 @@ open BigOperators
variable {n : ℕ}
open VectorLikeOddPlane
/-- A property on `LinSols`, satisfied if every point on the line between the two planes
/-- A property on `LinSols`, satisfied if every point on the line between the two planes
in the basis through that point is in the cubic. -/
def LineInCubic (S : (PureU1 (2 * n + 1)).LinSols) : Prop :=
∀ (g f : Fin n → ℚ) (_ : S.val = Pa g f) (a b : ℚ) ,
∀ (g f : Fin n → ℚ) (_ : S.val = Pa g f) (a b : ℚ) ,
accCube (2 * n + 1) (a • P g + b • P! f) = 0
lemma lineInCubic_expand {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S) :
@ -55,18 +55,18 @@ lemma lineInCubic_expand {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S)
ring
lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S) :
∀ (g : Fin n → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
∀ (g : Fin n → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
intro g f hS
linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1 ) -
(lineInCubic_expand h g f hS 1 2 ) / 6
/-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
/-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
def LineInCubicPerm (S : (PureU1 (2 * n + 1)).LinSols) : Prop :=
∀ (M : (FamilyPermutations (2 * n + 1)).group ),
LineInCubic ((FamilyPermutations (2 * n + 1)).linSolRep M S)
/-- If `lineInCubicPerm S` then `lineInCubic S`. -/
/-- If `lineInCubicPerm S` then `lineInCubic S`. -/
lemma lineInCubicPerm_self {S : (PureU1 (2 * n + 1)).LinSols} (hS : LineInCubicPerm S) :
LineInCubic S := hS 1
@ -89,7 +89,7 @@ lemma lineInCubicPerm_swap {S : (PureU1 (2 * n.succ + 1)).LinSols}
(S.val (δ!₂ j) - S.val (δ!₁ j))
* accCubeTriLinSymm (P g) (P g) (basis!AsCharges j) = 0 := by
intro j g f h
let S' := (FamilyPermutations (2 * n.succ + 1)).linSolRep
let S' := (FamilyPermutations (2 * n.succ + 1)).linSolRep
(pairSwap (δ!₁ j) (δ!₂ j)) S
have hSS' : ((FamilyPermutations (2 * n.succ + 1)).linSolRep
(pairSwap (δ!₁ j) (δ!₂ j))) S = S' := rfl
@ -119,7 +119,7 @@ lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
have h2 := Pa_δa₂ f g 0
rw [← hS] at h1 h2 h4
simp at h2
have h5 : f 1 = S.val (δa₂ 0) + S.val δa₁ + S.val (δa₄ 0):= by
have h5 : f 1 = S.val (δa₂ 0) + S.val δa₁ + S.val (δa₄ 0):= by
linear_combination -(1 * h1) - 1 * h4 - 1 * h2
rw [h5]
rw [δa₄_δ!₂]
@ -133,7 +133,7 @@ lemma lineInCubicPerm_last_cond {S : (PureU1 (2 * n.succ.succ+1)).LinSols}
(LIC : LineInCubicPerm S) :
LineInPlaneProp ((S.val (δ!₂ 0)), ((S.val (δ!₁ 0)), (S.val δ!₃))) := by
obtain ⟨g, f, hfg⟩ := span_basis S
have h1 := lineInCubicPerm_swap LIC 0 g f hfg
have h1 := lineInCubicPerm_swap LIC 0 g f hfg
rw [P_P_P!_accCube' g f hfg] at h1
simp at h1
cases h1 <;> rename_i h1
@ -147,7 +147,7 @@ lemma lineInCubicPerm_last_cond {S : (PureU1 (2 * n.succ.succ+1)).LinSols}
apply Or.inr
linear_combination h1
lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
(LIC : LineInCubicPerm S) : LineInPlaneCond S := by
refine @Prop_three (2 * n.succ.succ + 1) LineInPlaneProp S (δ!₂ 0) (δ!₁ 0)
δ!₃ ?_ ?_ ?_ ?_
@ -157,11 +157,11 @@ lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
intro M
exact lineInCubicPerm_last_cond (lineInCubicPerm_permute LIC M)
lemma lineInCubicPerm_constAbs {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
lemma lineInCubicPerm_constAbs {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
(LIC : LineInCubicPerm S) : ConstAbs S.val :=
linesInPlane_constAbs (lineInCubicPerm_last_perm LIC)
theorem lineInCubicPerm_zero {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
theorem lineInCubicPerm_zero {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
(LIC : LineInCubicPerm S) : S = 0 :=
ConstAbs.boundary_value_odd S (lineInCubicPerm_constAbs LIC)