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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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28
HepLean/AnomalyCancellation/Basic.lean
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@ -34,14 +34,14 @@ def ACCSystemChargesMk (n : ℕ) : ACCSystemCharges where
namespace ACCSystemCharges
/-- The charges as functions from `Fin χ.numberCharges → ℚ`. -/
def charges (χ : ACCSystemCharges) : Type := Fin χ.numberCharges → ℚ
def Charges (χ : ACCSystemCharges) : Type := Fin χ.numberCharges → ℚ
/--
An instance to provide the necessary operations and properties for `charges` to form an additive
commutative monoid.
-/
@[simps!]
instance chargesAddCommMonoid (χ : ACCSystemCharges) : AddCommMonoid χ.charges :=
instance chargesAddCommMonoid (χ : ACCSystemCharges) : AddCommMonoid χ.Charges :=
Pi.addCommMonoid
/--
@ -49,17 +49,17 @@ instance chargesAddCommMonoid (χ : ACCSystemCharges) : AddCommMonoid χ.charges
the field `ℚ`.
-/
@[simps!]
instance chargesModule (χ : ACCSystemCharges) : Module ℚ χ.charges :=
instance chargesModule (χ : ACCSystemCharges) : Module ℚ χ.Charges :=
Pi.module _ _ _
/--
An instance provides the necessary operations and properties for `charges` to form an additive
commutative group.
-/
instance ChargesAddCommGroup (χ : ACCSystemCharges) : AddCommGroup χ.charges :=
instance ChargesAddCommGroup (χ : ACCSystemCharges) : AddCommGroup χ.Charges :=
Module.addCommMonoidToAddCommGroup ℚ
instance (χ : ACCSystemCharges) : Module.Finite ℚ χ.charges :=
instance (χ : ACCSystemCharges) : Module.Finite ℚ χ.Charges :=
FiniteDimensional.finiteDimensional_pi ℚ
end ACCSystemCharges
@ -69,14 +69,14 @@ structure ACCSystemLinear extends ACCSystemCharges where
/-- The number of linear ACCs. -/
numberLinear : ℕ
/-- The linear ACCs. -/
linearACCs : Fin numberLinear → (toACCSystemCharges.charges →ₗ[ℚ] ℚ)
linearACCs : Fin numberLinear → (toACCSystemCharges.Charges →ₗ[ℚ] ℚ)
namespace ACCSystemLinear
/-- The type of solutions to the linear ACCs. -/
structure LinSols (χ : ACCSystemLinear) where
/-- The underlying charge. -/
val : χ.1.charges
val : χ.1.Charges
/-- The condition that the charge satisfies the linear ACCs. -/
linearSol : ∀ i : Fin χ.numberLinear, χ.linearACCs i val = 0
@ -154,7 +154,7 @@ instance linSolsAddCommGroup (χ : ACCSystemLinear) : AddCommGroup χ.LinSols :=
Module.addCommMonoidToAddCommGroup ℚ
/-- The inclusion of `LinSols` into `charges`. -/
def linSolsIncl (χ : ACCSystemLinear) : χ.LinSols →ₗ[ℚ] χ.charges where
def linSolsIncl (χ : ACCSystemLinear) : χ.LinSols →ₗ[ℚ] χ.Charges where
toFun S := S.val
map_add' _ _ := rfl
map_smul' _ _ := rfl
@ -166,7 +166,7 @@ structure ACCSystemQuad extends ACCSystemLinear where
/-- The number of quadratic ACCs. -/
numberQuadratic : ℕ
/-- The quadratic ACCs. -/
quadraticACCs : Fin numberQuadratic → HomogeneousQuadratic toACCSystemCharges.charges
quadraticACCs : Fin numberQuadratic → HomogeneousQuadratic toACCSystemCharges.Charges
namespace ACCSystemQuad
@ -211,7 +211,7 @@ def linSolsInclQuadSolsZero (χ : ACCSystemQuad) (h : χ.numberQuadratic = 0) :
map_smul' _ _ := rfl
/-- The inclusion of quadratic solutions into all charges. -/
def quadSolsIncl (χ : ACCSystemQuad) : χ.QuadSols →[ℚ] χ.charges :=
def quadSolsIncl (χ : ACCSystemQuad) : χ.QuadSols →[ℚ] χ.Charges :=
MulActionHom.comp χ.linSolsIncl.toMulActionHom χ.quadSolsInclLinSols
end ACCSystemQuad
@ -219,7 +219,7 @@ end ACCSystemQuad
/-- The type of charges plus the anomaly cancellation conditions. -/
structure ACCSystem extends ACCSystemQuad where
/-- The cubic ACC. -/
cubicACC : HomogeneousCubic toACCSystemCharges.charges
cubicACC : HomogeneousCubic toACCSystemCharges.Charges
namespace ACCSystem
@ -236,7 +236,7 @@ lemma Sols.ext {χ : ACCSystem} {S T : χ.Sols} (h : S.val = T.val) :
simp_all only
/-- We say a charge S is a solution if it extends to a solution. -/
def isSolution (χ : ACCSystem) (S : χ.charges) : Prop :=
def IsSolution (χ : ACCSystem) (S : χ.Charges) : Prop :=
∃ (sol : χ.Sols), sol.val = S
/-- An instance giving the properties and structures to define an action of `ℚ` on `Sols`. -/
@ -262,13 +262,13 @@ def solsInclLinSols (χ : ACCSystem) : χ.Sols →[ℚ] χ.LinSols :=
MulActionHom.comp χ.quadSolsInclLinSols χ.solsInclQuadSols
/-- The inclusion of `Sols` into `LinSols`. -/
def solsIncl (χ : ACCSystem) : χ.Sols →[ℚ] χ.charges :=
def solsIncl (χ : ACCSystem) : χ.Sols →[ℚ] χ.Charges :=
MulActionHom.comp χ.quadSolsIncl χ.solsInclQuadSols
/-- The structure of a map between two ACCSystems. -/
structure Hom (χ η : ACCSystem) where
/-- The linear map between vector spaces of charges. -/
charges : χ.charges →ₗ[ℚ] η.charges
charges : χ.Charges →ₗ[ℚ] η.Charges
/-- The map between solutions. -/
anomalyFree : χ.Sols → η.Sols
/-- The condition that the map commutes with the relevant inclusions. -/