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refactor: Change case of type and props

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jstoobysmith 2024-06-26 11:54:02 -04:00
parent 18b83f582e
commit f7a638d32e
58 changed files with 695 additions and 696 deletions
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22
HepLean/AnomalyCancellation/PureU1/Odd/Parameterization.lean
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@ -77,13 +77,13 @@ lemma anomalyFree_param {S : (PureU1 (2 * n + 1)).Sols}
/-- A proposition on a solution which is true if `accCubeTriLinSymm (P g, P g, P! f) ≠ 0`.
In this case our parameterization above will be able to recover this point. -/
def genericCase (S : (PureU1 (2 * n.succ + 1)).Sols) : Prop :=
def GenericCase (S : (PureU1 (2 * n.succ + 1)).Sols) : Prop :=
∀ (g f : Fin n.succ → ℚ) (_ : S.val = P g + P! f) ,
accCubeTriLinSymm (P g) (P g) (P! f) ≠ 0
lemma genericCase_exists (S : (PureU1 (2 * n.succ + 1)).Sols)
(hs : ∃ (g f : Fin n.succ → ℚ), S.val = P g + P! f ∧
accCubeTriLinSymm (P g) (P g) (P! f) ≠ 0) : genericCase S := by
accCubeTriLinSymm (P g) (P g) (P! f) ≠ 0) : GenericCase S := by
intro g f hS hC
obtain ⟨g', f', hS', hC'⟩ := hs
rw [hS] at hS'
@ -93,13 +93,13 @@ lemma genericCase_exists (S : (PureU1 (2 * n.succ + 1)).Sols)
/-- A proposition on a solution which is true if `accCubeTriLinSymm (P g, P g, P! f) ≠ 0`.
In this case we will show that S is zero if it is true for all permutations. -/
def specialCase (S : (PureU1 (2 * n.succ + 1)).Sols) : Prop :=
def SpecialCase (S : (PureU1 (2 * n.succ + 1)).Sols) : Prop :=
∀ (g f : Fin n.succ → ℚ) (_ : S.val = P g + P! f) ,
accCubeTriLinSymm (P g) (P g) (P! f) = 0
lemma specialCase_exists (S : (PureU1 (2 * n.succ + 1)).Sols)
(hs : ∃ (g f : Fin n.succ → ℚ), S.val = P g + P! f ∧
accCubeTriLinSymm (P g) (P g) (P! f) = 0) : specialCase S := by
accCubeTriLinSymm (P g) (P g) (P! f) = 0) : SpecialCase S := by
intro g f hS
obtain ⟨g', f', hS', hC'⟩ := hs
rw [hS] at hS'
@ -108,7 +108,7 @@ lemma specialCase_exists (S : (PureU1 (2 * n.succ + 1)).Sols)
exact hC'
lemma generic_or_special (S : (PureU1 (2 * n.succ + 1)).Sols) :
genericCase S ∨ specialCase S := by
GenericCase S ∨ SpecialCase S := by
obtain ⟨g, f, h⟩ := span_basis S.1.1
have h1 : accCubeTriLinSymm (P g) (P g) (P! f) ≠ 0 ∨
accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
@ -117,7 +117,7 @@ lemma generic_or_special (S : (PureU1 (2 * n.succ + 1)).Sols) :
exact Or.inl (genericCase_exists S ⟨g, f, h, h1⟩)
exact Or.inr (specialCase_exists S ⟨g, f, h, h1⟩)
theorem generic_case {S : (PureU1 (2 * n.succ + 1)).Sols} (h : genericCase S) :
theorem generic_case {S : (PureU1 (2 * n.succ + 1)).Sols} (h : GenericCase S) :
∃ g f a, S = parameterization g f a := by
obtain ⟨g, f, hS⟩ := span_basis S.1.1
use g, f, (accCubeTriLinSymm (P! f) (P! f) (P g))⁻¹
@ -135,8 +135,8 @@ theorem generic_case {S : (PureU1 (2 * n.succ + 1)).Sols} (h : genericCase S) :
lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ + 1)).Sols}
(h : specialCase S) :
lineInCubic S.1.1 := by
(h : SpecialCase S) :
LineInCubic S.1.1 := by
intro g f hS a b
erw [TriLinearSymm.toCubic_add]
rw [HomogeneousCubic.map_smul, HomogeneousCubic.map_smul]
@ -155,15 +155,15 @@ lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ + 1)).Sols}
lemma special_case_lineInCubic_perm {S : (PureU1 (2 * n.succ + 1)).Sols}
(h : ∀ (M : (FamilyPermutations (2 * n.succ + 1)).group),
specialCase ((FamilyPermutations (2 * n.succ + 1)).solAction.toFun S M)) :
lineInCubicPerm S.1.1 := by
SpecialCase ((FamilyPermutations (2 * n.succ + 1)).solAction.toFun S M)) :
LineInCubicPerm S.1.1 := by
intro M
have hM := special_case_lineInCubic (h M)
exact hM
theorem special_case {S : (PureU1 (2 * n.succ.succ + 1)).Sols}
(h : ∀ (M : (FamilyPermutations (2 * n.succ.succ + 1)).group),
specialCase ((FamilyPermutations (2 * n.succ.succ + 1)).solAction.toFun S M)) :
SpecialCase ((FamilyPermutations (2 * n.succ.succ + 1)).solAction.toFun S M)) :
S.1.1 = 0 := by
have ht := special_case_lineInCubic_perm h
exact lineInCubicPerm_zero ht