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Merge pull request #94 from HEPLean/Update-versions

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refactor: normalize initial white space
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Joseph Tooby-Smith 2024-07-22 06:53:04 -04:00 • committed by GitHub
commit 782f4929d1
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46 changed files with 176 additions and 168 deletions
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2
HepLean/AnomalyCancellation/Basic.lean
View file

@ -234,7 +234,7 @@ lemma Sols.ext {χ : ACCSystem} {S T : χ.Sols} (h : S.val = T.val) :
/-- A charge `S` is a solution if it extends to a solution. -/
def IsSolution (χ : ACCSystem) (S : χ.Charges) : Prop :=
∃ (sol : χ.Sols), sol.val = S
∃ (sol : χ.Sols), sol.val = S
/-- An instance giving the properties and structures to define an action of `ℚ` on `Sols`. -/
instance solsMulAction (χ : ACCSystem) : MulAction ℚ χ.Sols where

16
HepLean/AnomalyCancellation/GroupActions.lean
View file

@ -43,8 +43,8 @@ instance {χ : ACCSystem} (G : ACCSystemGroupAction χ) : Group G.group := G.gro
def linSolMap {χ : ACCSystem} (G : ACCSystemGroupAction χ) (g : G.group) :
χ.LinSols →ₗ[ℚ] χ.LinSols where
toFun S := ⟨G.rep g S.val, by
intro i
rw [G.linearInvariant, S.linearSol]⟩
intro i
rw [G.linearInvariant, S.linearSol]⟩
map_add' S T := by
apply ACCSystemLinear.LinSols.ext
exact (G.rep g).map_add' _ _
@ -82,9 +82,9 @@ lemma rep_linSolRep_commute {χ : ACCSystem} (G : ACCSystemGroupAction χ) (g :
instance quadSolAction {χ : ACCSystem} (G : ACCSystemGroupAction χ) :
MulAction G.group χ.QuadSols where
smul f S := ⟨G.linSolRep f S.1, by
intro i
simp only [linSolRep_apply_apply_val]
rw [G.quadInvariant, S.quadSol]⟩
intro i
simp only [linSolRep_apply_apply_val]
rw [G.quadInvariant, S.quadSol]⟩
mul_smul f1 f2 S := by
apply ACCSystemQuad.QuadSols.ext
change (G.rep.toFun (f1 * f2)) S.val = _
@ -107,9 +107,9 @@ lemma rep_quadSolAction_commute {χ : ACCSystem} (G : ACCSystemGroupAction χ) (
/-- The group action acting on solutions to the anomaly cancellation conditions. -/
instance solAction {χ : ACCSystem} (G : ACCSystemGroupAction χ) : MulAction G.group χ.Sols where
smul g S := ⟨G.quadSolAction.toFun S.1 g, by
simp only [MulAction.toFun_apply]
change χ.cubicACC (G.rep g S.val) = 0
rw [G.cubicInvariant, S.cubicSol]⟩
simp only [MulAction.toFun_apply]
change χ.cubicACC (G.rep g S.val) = 0
rw [G.cubicInvariant, S.cubicSol]⟩
mul_smul f1 f2 S := by
apply ACCSystem.Sols.ext
change (G.rep.toFun (f1 * f2)) S.val = _

4
HepLean/AnomalyCancellation/MSSMNu/Basic.lean
View file

@ -56,7 +56,7 @@ def toSplitSMPlusH : MSSMCharges.Charges ≃ (Fin 18 → ℚ) × (Fin 2 → ℚ)
/-- An equivalence between `(Fin 18 → ℚ)` and `(Fin 6 → Fin 3 → ℚ)`. -/
@[simps!]
def toSpeciesMaps' : (Fin 18 → ℚ) ≃ (Fin 6 → Fin 3 → ℚ) :=
((Equiv.curry _ _ _).symm.trans
((Equiv.curry _ _ _).symm.trans
((@finProdFinEquiv 6 3).arrowCongr (Equiv.refl ℚ))).symm
/-- An equivalence between `MSSMCharges.charges` and `(Fin 6 → Fin 3 → ℚ) × (Fin 2 → ℚ))`.
@ -367,7 +367,7 @@ lemma cubeTriLinToFun_map_add₁ (S T R L : MSSMCharges.Charges) :
rw [add_comm (2 * Hd S * Hd R * Hd L + 2 * Hu S * Hu R * Hu L) _]
rw [add_assoc]
rw [← add_assoc _ _ (2 * Hd S * Hd R * Hd L + 2 * Hu S * Hu R * Hu L +
(2 * Hd T * Hd R * Hd L + 2 * Hu T * Hu R * Hu L))]
(2 * Hd T * Hd R * Hd L + 2 * Hu T * Hu R * Hu L))]
congr 1
rw [← Finset.sum_add_distrib]
apply Fintype.sum_congr

6
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/Basic.lean
View file

@ -109,8 +109,8 @@ lemma quad_self_proj (T : MSSMACC.Sols) :
lemma quad_proj (T : MSSMACC.Sols) :
quadBiLin (proj T.1.1).val (proj T.1.1).val = 2 * dot Y₃.val B₃.val *
((dot B₃.val T.val - dot Y₃.val T.val) * quadBiLin Y₃.val T.val +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * quadBiLin B₃.val T.val) := by
((dot B₃.val T.val - dot Y₃.val T.val) * quadBiLin Y₃.val T.val +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * quadBiLin B₃.val T.val) := by
nth_rewrite 1 [proj_val]
repeat rw [quadBiLin.map_add₁]
repeat rw [quadBiLin.map_smul₁]
@ -151,7 +151,7 @@ lemma cube_proj_proj_B₃ (T : MSSMACC.LinSols) :
rw [cubeTriLin.map_add₂, cubeTriLin.map_smul₁, cubeTriLin.map_smul₂]
rw [cubeTriLin.swap₁, cubeTriLin.swap₂, doublePoint_Y₃_B₃]
rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂, cubeTriLin.swap₁, cubeTriLin.swap₂,
cubeTriLin.swap₁, doublePoint_B₃_B₃]
cubeTriLin.swap₁, doublePoint_B₃_B₃]
rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂]
ring

2
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/PlaneWithY3B3.lean
View file

@ -48,7 +48,7 @@ lemma planeY₃B₃_eq (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) (h : a = a'
lemma planeY₃B₃_val_eq' (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) (hR' : R.val ≠ 0)
(h : (planeY₃B₃ R a b c).val = (planeY₃B₃ R a' b' c').val) :
a = a' ∧ b = b' ∧ c = c' := by
a = a' ∧ b = b' ∧ c = c' := by
rw [planeY₃B₃_val, planeY₃B₃_val] at h
have h1 := congrArg (fun S => dot Y₃.val S) h
have h2 := congrArg (fun S => dot B₃.val S) h

7
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean
View file

@ -43,7 +43,7 @@ instance (R : MSSMACC.AnomalyFreePerp) : Decidable (LineEqProp R) := by
apply And.decidable
/-- A condition on `Sols` which we will show in `linEqPropSol_iff_proj_linEqProp` that is equivalent
to the condition that the `proj` of the solution satisfies `lineEqProp`. -/
to the condition that the `proj` of the solution satisfies `lineEqProp`. -/
def LineEqPropSol (R : MSSMACC.Sols) : Prop :=
cubeTriLin R.val R.val Y₃.val * quadBiLin B₃.val R.val -
cubeTriLin R.val R.val B₃.val * quadBiLin Y₃.val R.val = 0
@ -338,8 +338,7 @@ lemma inQuadToSol_proj (T : InQuadSol) : inQuadToSol (inQuadProj T) = T.val := b
ring_nf
simp only [zero_smul, add_zero, Fin.isValue, Fin.reduceFinMk, zero_add]
have h1 : (cubeTriLin T.val.val T.val.val Y₃.val ^ 2 * dot Y₃.val B₃.val ^ 3 * 3 +
dot Y₃.val B₃.val ^ 3 * cubeTriLin T.val.val T.val.val B₃.val ^ 2
* 3) = cubicCoeff T.val := by
dot Y₃.val B₃.val ^ 3 * cubeTriLin T.val.val T.val.val B₃.val ^ 2* 3) = cubicCoeff T.val := by
rw [cubicCoeff]
ring
rw [h1]
@ -360,7 +359,7 @@ def inQuadCubeToSol : InQuadCube × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R
simp)
lemma inQuadCubeToSol_smul (R : InQuadCube) (c₁ c₂ c₃ d : ℚ) :
inQuadCubeToSol (R, (d * c₁), (d * c₂), (d * c₃)) = d • inQuadCubeToSol (R, c₁, c₂, c₃):= by
inQuadCubeToSol (R, (d * c₁), (d * c₂), (d * c₃)) = d • inQuadCubeToSol (R, c₁, c₂, c₃) := by
apply ACCSystem.Sols.ext
change (planeY₃B₃ _ _ _ _).val = _
rw [planeY₃B₃_smul]

6
HepLean/AnomalyCancellation/PureU1/Basic.lean
View file

@ -31,8 +31,8 @@ def accGrav (n : ℕ) : ((PureU1Charges n).Charges →ₗ[ℚ] ℚ) where
toFun S := ∑ i : Fin n, S i
map_add' S T := Finset.sum_add_distrib
map_smul' a S := by
simp [HSMul.hSMul, SMul.smul]
rw [← Finset.mul_sum]
simp [HSMul.hSMul, SMul.smul]
rw [← Finset.mul_sum]
/-- The symmetric trilinear form used to define the cubic anomaly. -/
@[simps!]
@ -95,7 +95,7 @@ def PureU1 (n : ℕ) : ACCSystem where
cubicACC := PureU1.accCube n
/-- An equivalence of vector spaces of charges when the number of fermions is equal. -/
def pureU1EqCharges {n m : ℕ} (h : n = m):
def pureU1EqCharges {n m : ℕ} (h : n = m) :
(PureU1 n).Charges ≃ₗ[ℚ] (PureU1 m).Charges where
toFun f := f ∘ Fin.cast h.symm
invFun f := f ∘ Fin.cast h

15
HepLean/AnomalyCancellation/PureU1/BasisLinear.lean
View file

@ -24,14 +24,11 @@ namespace BasisLinear
last position. -/
@[simp]
def asCharges (j : Fin n) : (PureU1 n.succ).Charges :=
(fun i =>
if i = j.castSucc then
1
else
if i = Fin.last n then
- 1
else
0)
(fun i =>
if i = j.castSucc then 1
else if i = Fin.last n then
- 1
else 0)
lemma asCharges_eq_castSucc (j : Fin n) :
asCharges j (Fin.castSucc j) = 1 := by
@ -123,7 +120,7 @@ def asBasis : Basis (Fin n) ℚ ((PureU1 n.succ).LinSols) where
repr := coordinateMap
instance : Module.Finite ℚ ((PureU1 n.succ).LinSols) :=
Module.Finite.of_basis asBasis
Module.Finite.of_basis asBasis
lemma finrank_AnomalyFreeLinear :
FiniteDimensional.finrank ℚ (((PureU1 n.succ).LinSols)) = n := by

2
HepLean/AnomalyCancellation/PureU1/ConstAbs.lean
View file

@ -96,7 +96,7 @@ lemma is_zero (h0 : S (0 : Fin n.succ) = 0) : S = 0 := by
/-- A boundary of `S : (PureU1 n.succ).charges` (assumed sorted, constAbs and non-zero)
is defined as a element of `k ∈ Fin n` such that `S k.castSucc` and `S k.succ` are different signs.
-/
-/
@[simp]
def Boundary (S : (PureU1 n.succ).Charges) (k : Fin n) : Prop := S k.castSucc < 0 ∧ 0 < S k.succ

24
HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean
View file

@ -550,7 +550,7 @@ def Pa' (f : (Fin n.succ) ⊕ (Fin n) → ℚ) : (PureU1 (2 * n.succ)).LinSols :
∑ i, f i • basisa i
lemma Pa'_P'_P!' (f : (Fin n.succ) ⊕ (Fin n) → ℚ) :
Pa' f = P' (f ∘ Sum.inl) + P!' (f ∘ Sum.inr):= by
Pa' f = P' (f ∘ Sum.inl) + P!' (f ∘ Sum.inr) := by
exact Fintype.sum_sum_type _
lemma P'_val (f : Fin n.succ → ℚ) : (P' f).val = P f := by
@ -617,7 +617,7 @@ lemma Pa'_eq (f f' : (Fin n.succ) ⊕ (Fin n) → ℚ) : Pa' f = Pa' f' ↔ f =
simp
have h2 : ∀ i, (f i + (- f' i)) = 0 := by
exact Fintype.linearIndependent_iff.mp (@basisa_linear_independent n)
(fun i => f i + -f' i) h1
(fun i => f i + -f' i) h1
have h2i := h2 i
linarith
intro h
@ -685,9 +685,9 @@ lemma span_basis (S : (PureU1 (2 * n.succ)).LinSols) :
rfl
lemma P!_in_span (f : Fin n → ℚ) : P! f ∈ Submodule.span ℚ (Set.range basis!AsCharges) := by
rw [(mem_span_range_iff_exists_fun ℚ)]
use f
rfl
rw [(mem_span_range_iff_exists_fun ℚ)]
use f
rfl
lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ)).LinSols) (j : Fin n) :
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∈
@ -700,11 +700,9 @@ lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ)).LinSols) (j : Fin
lemma span_basis_swap! {S : (PureU1 (2 * n.succ)).LinSols} (j : Fin n)
(hS : ((FamilyPermutations (2 * n.succ)).linSolRep
(pairSwap (δ!₁ j) (δ!₂ j))) S = S') (g : Fin n.succ → ℚ) (f : Fin n → ℚ)
(h : S.val = P g + P! f):
∃
(g' : Fin n.succ → ℚ) (f' : Fin n → ℚ),
S'.val = P g' + P! f' ∧ P! f' = P! f +
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∧ g' = g := by
(h : S.val = P g + P! f) : ∃ (g' : Fin n.succ → ℚ) (f' : Fin n → ℚ),
S'.val = P g' + P! f' ∧ P! f' = P! f +
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∧ g' = g := by
let X := P! f + (S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j
have hX : X ∈ Submodule.span ℚ (Set.range (basis!AsCharges)) := by
apply Submodule.add_mem
@ -723,10 +721,8 @@ lemma span_basis_swap! {S : (PureU1 (2 * n.succ)).LinSols} (j : Fin n)
exact hS
lemma vectorLikeEven_in_span (S : (PureU1 (2 * n.succ)).LinSols)
(hS : VectorLikeEven S.val) :
∃ (M : (FamilyPermutations (2 * n.succ)).group),
(FamilyPermutations (2 * n.succ)).linSolRep M S
∈ Submodule.span ℚ (Set.range basis) := by
(hS : VectorLikeEven S.val) : ∃ (M : (FamilyPermutations (2 * n.succ)).group),
(FamilyPermutations (2 * n.succ)).linSolRep M S ∈ Submodule.span ℚ (Set.range basis) := by
use (Tuple.sort S.val).symm
change sortAFL S ∈ Submodule.span ℚ (Set.range basis)
rw [mem_span_range_iff_exists_fun ℚ]

12
HepLean/AnomalyCancellation/PureU1/Even/LineInCubic.lean
View file

@ -49,23 +49,23 @@ lemma lineInCubic_expand {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic S)
change accCubeTriLinSymm.toCubic (a • P g + b • P! f) = 0 at h1
simp only [TriLinearSymm.toCubic_add] at h1
simp only [HomogeneousCubic.map_smul,
accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1
accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1
erw [P_accCube, P!_accCube] at h1
rw [← h1]
ring
/--
This lemma states that for a given `S` of type `(PureU1 (2 * n.succ)).AnomalyFreeLinear` and
a proof `h` that the line through `S` lies on a cubic curve,
for any functions `g : Fin n.succ → ℚ` and `f : Fin n → ℚ`, if `S.val = P g + P! f`,
then `accCubeTriLinSymm.toFun (P g, P g, P! f) = 0`.
This lemma states that for a given `S` of type `(PureU1 (2 * n.succ)).AnomalyFreeLinear` and
a proof `h` that the line through `S` lies on a cubic curve,
for any functions `g : Fin n.succ → ℚ` and `f : Fin n → ℚ`, if `S.val = P g + P! f`,
then `accCubeTriLinSymm.toFun (P g, P g, P! f) = 0`.
-/
lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic S) :
∀ (g : Fin n.succ → 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
(lineInCubic_expand h g f hS 1 2) / 6
/-- A `LinSol` satisfies `LineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
def LineInCubicPerm (S : (PureU1 (2 * n.succ)).LinSols) : Prop :=

12
HepLean/AnomalyCancellation/PureU1/Even/Parameterization.lean
View file

@ -49,15 +49,15 @@ lemma parameterizationAsLinear_val (g : Fin n.succ → ℚ) (f : Fin n → ℚ)
change a • (_ • (P' g).val + _ • (P!' f).val) = _
rw [P'_val, P!'_val]
lemma parameterizationCharge_cube (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (a : ℚ):
lemma parameterizationCharge_cube (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (a : ℚ) :
accCube (2* n.succ) (parameterizationAsLinear g f a).val = 0 := by
change accCubeTriLinSymm.toCubic _ = 0
rw [parameterizationAsLinear_val, HomogeneousCubic.map_smul,
TriLinearSymm.toCubic_add, HomogeneousCubic.map_smul, HomogeneousCubic.map_smul]
erw [P_accCube, P!_accCube]
rw [accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
ring
/-- The construction of a `Sol` from a `Fin n.succ → ℚ`, a `Fin n → ℚ` and a `ℚ`. -/
@ -112,7 +112,7 @@ lemma generic_or_special (S : (PureU1 (2 * n.succ)).Sols) :
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
accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
exact ne_or_eq _ _
cases h1 <;> rename_i h1
exact Or.inl (genericCase_exists S ⟨g, f, h, h1⟩)
@ -142,8 +142,8 @@ lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ)).Sols}
erw [P_accCube, P!_accCube]
have h := h g f hS
rw [accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
rw [h]
rw [anomalyFree_param _ _ hS] at h
simp at h

2
HepLean/AnomalyCancellation/PureU1/LineInPlaneCond.lean
View file

@ -89,7 +89,7 @@ lemma lineInPlaneCond_eq_last {S : (PureU1 (n.succ.succ.succ.succ.succ)).LinSols
intro a
linarith
have ht : S.val ((Fin.last n.succ.succ.succ).succ) =
- S.val ((Fin.last n.succ.succ.succ).castSucc) := by
- S.val ((Fin.last n.succ.succ.succ).castSucc) := by
rw [← mul_right_inj' hx]
simp [Nat.succ_eq_add_one]
simp at h

14
HepLean/AnomalyCancellation/PureU1/Odd/BasisLinear.lean
View file

@ -535,7 +535,7 @@ def Pa' (f : (Fin n) ⊕ (Fin n) → ℚ) : (PureU1 (2 * n + 1)).LinSols :=
∑ i, f i • basisa i
lemma Pa'_P'_P!' (f : (Fin n) ⊕ (Fin n) → ℚ) :
Pa' f = P' (f ∘ Sum.inl) + P!' (f ∘ Sum.inr):= by
Pa' f = P' (f ∘ Sum.inl) + P!' (f ∘ Sum.inr) := by
exact Fintype.sum_sum_type _
lemma P'_val (f : Fin n → ℚ) : (P' f).val = P f := by
@ -602,7 +602,7 @@ lemma Pa'_eq (f f' : (Fin n.succ) ⊕ (Fin n.succ) → ℚ) : Pa' f = Pa' f' ↔
simp
have h2 : ∀ i, (f i + (- f' i)) = 0 := by
exact Fintype.linearIndependent_iff.mp (@basisa_linear_independent n)
(fun i => f i + -f' i) h1
(fun i => f i + -f' i) h1
have h2i := h2 i
linarith
intro h
@ -671,15 +671,15 @@ lemma span_basis (S : (PureU1 (2 * n.succ + 1)).LinSols) :
lemma span_basis_swap! {S : (PureU1 (2 * n.succ + 1)).LinSols} (j : Fin n.succ)
(hS : ((FamilyPermutations (2 * n.succ + 1)).linSolRep
(pairSwap (δ!₁ j) (δ!₂ j))) S = S') (g f : Fin n.succ → ℚ) (hS1 : S.val = P g + P! f):
(pairSwap (δ!₁ j) (δ!₂ j))) S = S') (g f : Fin n.succ → ℚ) (hS1 : S.val = P g + P! f) :
∃ (g' f' : Fin n.succ → ℚ),
S'.val = P g' + P! f' ∧ P! f' = P! f +
S'.val = P g' + P! f' ∧ P! f' = P! f +
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∧ g' = g := by
let X := P! f + (S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j
have hf : P! f ∈ Submodule.span ℚ (Set.range basis!AsCharges) := by
rw [(mem_span_range_iff_exists_fun ℚ)]
use f
rfl
rw [(mem_span_range_iff_exists_fun ℚ)]
use f
rfl
have hP : (S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∈
Submodule.span ℚ (Set.range basis!AsCharges) := by
apply Submodule.smul_mem

8
HepLean/AnomalyCancellation/PureU1/Odd/LineInCubic.lean
View file

@ -49,7 +49,7 @@ lemma lineInCubic_expand {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S)
change accCubeTriLinSymm.toCubic (a • P g + b • P! f) = 0 at h1
simp only [TriLinearSymm.toCubic_add] at h1
simp only [HomogeneousCubic.map_smul,
accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1
accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂, accCubeTriLinSymm.map_smul₃] at h1
erw [P_accCube, P!_accCube] at h1
rw [← h1]
ring
@ -59,7 +59,7 @@ lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S
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
(lineInCubic_expand h g f hS 1 2) / 6
/-- A `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
def LineInCubicPerm (S : (PureU1 (2 * n + 1)).LinSols) : Prop :=
@ -119,8 +119,8 @@ 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
linear_combination -(1 * h1) - 1 * h4 - 1 * h2
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]
have h0 : (δa₂ (0 : Fin n.succ)) = δ!₁ 0 := by

12
HepLean/AnomalyCancellation/PureU1/Odd/Parameterization.lean
View file

@ -44,7 +44,7 @@ lemma parameterizationAsLinear_val (g f : Fin n → ℚ) (a : ℚ) :
change a • (_ • (P' g).val + _ • (P!' f).val) = _
rw [P'_val, P!'_val]
lemma parameterizationCharge_cube (g f : Fin n → ℚ) (a : ℚ):
lemma parameterizationCharge_cube (g f : Fin n → ℚ) (a : ℚ) :
(accCube (2 * n + 1)) (parameterizationAsLinear g f a).val = 0 := by
change accCubeTriLinSymm.toCubic _ = 0
rw [parameterizationAsLinear_val]
@ -53,8 +53,8 @@ lemma parameterizationCharge_cube (g f : Fin n → ℚ) (a : ℚ):
rw [HomogeneousCubic.map_smul, HomogeneousCubic.map_smul]
erw [P_accCube g, P!_accCube f]
rw [accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
ring
/-- Given a `g f : Fin n → ℚ` and a `a : ℚ` we form a solution. -/
@ -111,7 +111,7 @@ lemma generic_or_special (S : (PureU1 (2 * n.succ + 1)).Sols) :
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
accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
exact ne_or_eq _ _
cases h1 <;> rename_i h1
exact Or.inl (genericCase_exists S ⟨g, f, h, h1⟩)
@ -143,8 +143,8 @@ lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ + 1)).Sols}
erw [P!_accCube]
have h := h g f hS
rw [accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
accCubeTriLinSymm.map_smul₃]
rw [h]
rw [anomalyFree_param _ _ hS] at h
simp at h

10
HepLean/AnomalyCancellation/PureU1/Permutations.lean
View file

@ -310,8 +310,8 @@ lemma Prop_two (P : ℚ × ℚ → Prop) {S : (PureU1 n).LinSols}
rw [FamilyPermutations_anomalyFreeLinear_apply, FamilyPermutations_anomalyFreeLinear_apply] at h1
simp at h1
change P
(S.val ((permTwo hij hab).toFun a),
S.val ((permTwo hij hab).toFun b)) at h1
(S.val ((permTwo hij hab).toFun a),
S.val ((permTwo hij hab).toFun b)) at h1
erw [permTwo_fst,permTwo_snd] at h1
exact h1
@ -325,11 +325,11 @@ lemma Prop_three (P : ℚ × ℚ × ℚ → Prop) {S : (PureU1 n).LinSols}
intro i j k hij hjk hik
have h1 := h (permThree hij hjk hik hab hbc hac).symm
rw [FamilyPermutations_anomalyFreeLinear_apply, FamilyPermutations_anomalyFreeLinear_apply,
FamilyPermutations_anomalyFreeLinear_apply] at h1
FamilyPermutations_anomalyFreeLinear_apply] at h1
simp at h1
change P
(S.val ((permThree hij hjk hik hab hbc hac).toFun a),
S.val ((permThree hij hjk hik hab hbc hac).toFun b),
(S.val ((permThree hij hjk hik hab hbc hac).toFun a),
S.val ((permThree hij hjk hik hab hbc hac).toFun b),
S.val ((permThree hij hjk hik hab hbc hac).toFun c)) at h1
erw [permThree_fst,permThree_snd, permThree_thd] at h1
exact h1

2
HepLean/AnomalyCancellation/PureU1/Sort.lean
View file

@ -24,7 +24,7 @@ variable {n : ℕ}
/-- A charge is sorted if for all `i ≤ j`, then `S i ≤ S j`. -/
@[simp]
def Sorted {n : ℕ} (S : (PureU1 n).Charges) : Prop :=
∀ i j (_ : i ≤ j), S i ≤ S j
∀ i j (_ : i ≤ j), S i ≤ S j
/-- Given a charge assignment `S`, the corresponding sorted charge assignment. -/
@[simp]

2
HepLean/AnomalyCancellation/SM/NoGrav/One/Lemmas.lean
View file

@ -46,7 +46,7 @@ lemma accGrav_Q_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) = 0) :
have h1 := SU2Sol S.1.1
have h2 := SU3Sol S.1.1
simp only [accSU2, SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
Finset.sum_singleton, LinearMap.coe_mk, AddHom.coe_mk, accSU3] at h1 h2
Finset.sum_singleton, LinearMap.coe_mk, AddHom.coe_mk, accSU3] at h1 h2
erw [hQ] at h1 h2
simp_all
linear_combination 3 * h2

8
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
View file

@ -116,8 +116,8 @@ lemma cubic_zero_E'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
toFun S := S.asLinear
invFun S := ⟨SMCharges.Q S.val (0 : Fin 1), (SMCharges.U S.val (0 : Fin 1) -
SMCharges.D S.val (0 : Fin 1))/2,
SMCharges.E S.val (0 : Fin 1)⟩
SMCharges.D S.val (0 : Fin 1))/2,
SMCharges.E S.val (0 : Fin 1)⟩
left_inv S := by
apply linearParameters.ext
rfl
@ -134,7 +134,7 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
intro i
rw [asLinear_val]
funext j
have hj : j = (0 : Fin 1):= by
have hj : j = (0 : Fin 1) := by
simp only [Fin.isValue]
ext
simp
@ -284,7 +284,7 @@ lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection
(FLTThree : FermatLastTheoremWith ℚ 3) :
S.v = 0 ∨ S.w = 0 := by
rw [S.cubic] at h
have h1 : (-1)^3 = (-1 : ℚ):= by rfl
have h1 : (-1)^3 = (-1 : ℚ) := by rfl
rw [← h1] at h
by_contra hn
simp [not_or] at hn

2
HepLean/AnomalyCancellation/SM/Permutations.lean
View file

@ -70,7 +70,7 @@ lemma toSpecies_sum_invariant (m : ℕ) (f : PermGroup n) (S : (SMCharges n).Cha
∑ i, ((fun a => a ^ m) ∘ toSpecies j S) i := by
rw [repCharges_toSpecies]
exact Fintype.sum_equiv (f⁻¹ j) (fun x => ((fun a => a ^ m) ∘ (toSpecies j) S ∘ ⇑(f⁻¹ j)) x)
(fun x => ((fun a => a ^ m) ∘ (toSpecies j) S) x) (congrFun rfl)
(fun x => ((fun a => a ^ m) ∘ (toSpecies j) S) x) (congrFun rfl)
lemma accGrav_invariant (f : PermGroup n) (S : (SMCharges n).Charges) :
accGrav (repCharges f S) = accGrav S :=

2
HepLean/AnomalyCancellation/SMNu/Basic.lean
View file

@ -260,7 +260,7 @@ def quadBiLin : BiLinearSymm (SMνCharges n).Charges := BiLinearSymm.mk₂
lemma quadBiLin_decomp (S T : (SMνCharges n).Charges) :
quadBiLin S T = ∑ i, Q S i * Q T i - 2 * ∑ i, U S i * U T i +
∑ i, D S i * D T i - ∑ i, L S i * L T i + ∑ i, E S i * E T i := by
∑ i, D S i * D T i - ∑ i, L S i * L T i + ∑ i, E S i * E T i := by
erw [← quadBiLin.toFun_eq_coe]
rw [quadBiLin]
simp only [quadBiLin, BiLinearSymm.mk₂, AddHom.toFun_eq_coe, AddHom.coe_mk, LinearMap.coe_mk]

2
HepLean/AnomalyCancellation/SMNu/FamilyMaps.lean
View file

@ -213,7 +213,7 @@ lemma familyUniversal_cubeTriLin (S : (SMνCharges 1).Charges) (T R : (SMνCharg
lemma familyUniversal_cubeTriLin' (S T : (SMνCharges 1).Charges) (R : (SMνCharges n).Charges) :
cubeTriLin (familyUniversal n S) (familyUniversal n T) R =
6 * S (0 : Fin 6) * T (0 : Fin 6) * ∑ i, Q R i +
3 * S (1 : Fin 6) * T (1 : Fin 6) * ∑ i, U R i
3 * S (1 : Fin 6) * T (1 : Fin 6) * ∑ i, U R i
+ 3 * S (2 : Fin 6) * T (2 : Fin 6) * ∑ i, D R i +
2 * S (3 : Fin 6) * T (3 : Fin 6) * ∑ i, L R i +
S (4 : Fin 6) * T (4 : Fin 6) * ∑ i, E R i + S (5 : Fin 6) * T (5 : Fin 6) * ∑ i, N R i := by

2
HepLean/AnomalyCancellation/SMNu/PlusU1/BMinusL.lean
View file

@ -86,7 +86,7 @@ lemma add_quad (S : (PlusU1 n).QuadSols) (a b : ℚ) :
def addQuad (S : (PlusU1 n).QuadSols) (a b : ℚ) : (PlusU1 n).QuadSols :=
linearToQuad (a • S.1 + b • (BL n).1.1) (add_quad S a b)
lemma addQuad_zero (S : (PlusU1 n).QuadSols) (a : ℚ): addQuad S a 0 = a • S := by
lemma addQuad_zero (S : (PlusU1 n).QuadSols) (a : ℚ) : addQuad S a 0 = a • S := by
simp [addQuad, linearToQuad]
rfl

4
HepLean/AnomalyCancellation/SMNu/PlusU1/BoundPlaneDim.lean
View file

@ -24,7 +24,7 @@ open BigOperators
/-- A proposition which is true if for a given `n`, a plane of charges of dimension `n` exists
in which each point is a solution. -/
def ExistsPlane (n : ℕ) : Prop := ∃ (B : Fin n → (PlusU1 3).Charges),
LinearIndependent ℚ B ∧ ∀ (f : Fin n → ℚ), (PlusU1 3).IsSolution (∑ i, f i • B i)
LinearIndependent ℚ B ∧ ∀ (f : Fin n → ℚ), (PlusU1 3).IsSolution (∑ i, f i • B i)
lemma exists_plane_exists_basis {n : ℕ} (hE : ExistsPlane n) :
∃ (B : Fin 11 ⊕ Fin n → (PlusU1 3).Charges), LinearIndependent ℚ B := by
@ -38,7 +38,7 @@ lemma exists_plane_exists_basis {n : ℕ} (hE : ExistsPlane n) :
rw [@add_eq_zero_iff_eq_neg] at hg
rw [← @Finset.sum_neg_distrib] at hg
have h1 : ∑ x : Fin n, -(g (Sum.inr x) • Y (Sum.inr x)) =
∑ x : Fin n, (-g (Sum.inr x)) • Y (Sum.inr x):= by
∑ x : Fin n, (-g (Sum.inr x)) • Y (Sum.inr x) := by
apply Finset.sum_congr
simp only
intro i _

2
HepLean/AnomalyCancellation/SMNu/PlusU1/HyperCharge.lean
View file

@ -84,7 +84,7 @@ lemma add_quad (S : (PlusU1 n).QuadSols) (a b : ℚ) :
def addQuad (S : (PlusU1 n).QuadSols) (a b : ℚ) : (PlusU1 n).QuadSols :=
linearToQuad (a • S.1 + b • (Y n).1.1) (add_quad S a b)
lemma addQuad_zero (S : (PlusU1 n).QuadSols) (a : ℚ): addQuad S a 0 = a • S := by
lemma addQuad_zero (S : (PlusU1 n).QuadSols) (a : ℚ) : addQuad S a 0 = a • S := by
simp [addQuad, linearToQuad]
rfl

14
HepLean/FeynmanDiagrams/Basic.lean
View file

@ -92,7 +92,7 @@ def preimageType' {𝓥 : Type} (v : 𝓥) : Over 𝓥 ⥤ Type where
def preimageVertex {𝓔 𝓥 : Type} (v : 𝓥) :
Over (P.HalfEdgeLabel × 𝓔 × 𝓥) ⥤ Over P.HalfEdgeLabel where
obj f := Over.mk (fun x => Prod.fst (f.hom x.1) :
(P.toVertex ⋙ preimageType' v).obj f ⟶ P.HalfEdgeLabel)
(P.toVertex ⋙ preimageType' v).obj f ⟶ P.HalfEdgeLabel)
map {f g} F := Over.homMk ((P.toVertex ⋙ preimageType' v).map F)
(funext <| fun x => congrArg Prod.fst <| congrFun F.w x.1)
@ -101,7 +101,7 @@ def preimageVertex {𝓔 𝓥 : Type} (v : 𝓥) :
def preimageEdge {𝓔 𝓥 : Type} (v : 𝓔) :
Over (P.HalfEdgeLabel × 𝓔 × 𝓥) ⥤ Over P.HalfEdgeLabel where
obj f := Over.mk (fun x => Prod.fst (f.hom x.1) :
(P.toEdge ⋙ preimageType' v).obj f ⟶ P.HalfEdgeLabel)
(P.toEdge ⋙ preimageType' v).obj f ⟶ P.HalfEdgeLabel)
map {f g} F := Over.homMk ((P.toEdge ⋙ preimageType' v).map F)
(funext <| fun x => congrArg Prod.fst <| congrFun F.w x.1)
@ -173,11 +173,11 @@ instance preimageEdgeDecidablePred {𝓔 𝓥 : Type} [DecidableEq 𝓔] (v :
| isFalse h => isFalse h
instance preimageVertexDecidable {𝓔 𝓥 : Type} (v : 𝓥)
(F : Over (P.HalfEdgeLabel × 𝓔 × 𝓥)) [DecidableEq F.left] :
(F : Over (P.HalfEdgeLabel × 𝓔 × 𝓥)) [DecidableEq F.left] :
DecidableEq ((P.preimageVertex v).obj F).left := Subtype.instDecidableEq
instance preimageEdgeDecidable {𝓔 𝓥 : Type} (v : 𝓔)
(F : Over (P.HalfEdgeLabel × 𝓔 × 𝓥)) [DecidableEq F.left] :
(F : Over (P.HalfEdgeLabel × 𝓔 × 𝓥)) [DecidableEq F.left] :
DecidableEq ((P.preimageEdge v).obj F).left := Subtype.instDecidableEq
instance preimageVertexFintype {𝓔 𝓥 : Type} [DecidableEq 𝓥]
@ -378,7 +378,7 @@ instance CondDecidable [IsFinitePreFeynmanRule P] {𝓔 𝓥 𝓱𝓔 : Type} (
/-- Making a Feynman diagram from maps of edges, vertices and half-edges. -/
def mk' {𝓔 𝓥 𝓱𝓔 : Type} (𝓔𝓞 : 𝓔 → P.EdgeLabel) (𝓥𝓞 : 𝓥 → P.VertexLabel)
(𝓱𝓔To𝓔𝓥 : 𝓱𝓔 → P.HalfEdgeLabel × 𝓔 × 𝓥)
(C : Cond 𝓔𝓞 𝓥𝓞 𝓱𝓔To𝓔𝓥): FeynmanDiagram P where
(C : Cond 𝓔𝓞 𝓥𝓞 𝓱𝓔To𝓔𝓥) : FeynmanDiagram P where
𝓔𝓞 := Over.mk 𝓔𝓞
𝓥𝓞 := Over.mk 𝓥𝓞
𝓱𝓔To𝓔𝓥 := Over.mk 𝓱𝓔To𝓔𝓥
@ -674,7 +674,7 @@ instance [IsFinitePreFeynmanRule P] [IsFiniteDiagram F] : Fintype F.SymmetryType
Fintype.ofEquiv _ F.symmetryTypeEquiv.symm
/-- The symmetry factor can be defined as the cardinal of the symmetry type.
In general this is not a finite number. -/
In general this is not a finite number. -/
@[simp]
def cardSymmetryFactor : Cardinal := Cardinal.mk (F.SymmetryType)
@ -705,7 +705,7 @@ A feynman diagram is connected if its simple graph is connected.
-/
/-- A relation on the vertices of Feynman diagrams. The proposition is true if the two
vertices are not equal and are connected by a single edge. -/
vertices are not equal and are connected by a single edge. -/
@[simp]
def AdjRelation : F.𝓥 → F.𝓥 → Prop := fun x y =>
x ≠ y ∧

12
HepLean/FeynmanDiagrams/Momentum.lean
View file

@ -45,7 +45,7 @@ We define the direct sum of the edge and vertex momentum spaces.
-/
/-- The type which assocaites to each half-edge a `1`-dimensional vector space.
Corresponding to that spanned by its momentum. -/
Corresponding to that spanned by its momentum. -/
def HalfEdgeMomenta : Type := F.𝓱𝓔 → ℝ
instance : AddCommGroup F.HalfEdgeMomenta := Pi.addCommGroup
@ -78,7 +78,7 @@ def euclidInner : F.HalfEdgeMomenta →ₗ[ℝ] F.HalfEdgeMomenta →ₗ[ℝ]
LinearMap.smul_apply]
/-- The type which associates to each edge a `1`-dimensional vector space.
Corresponding to that spanned by its total outflowing momentum. -/
Corresponding to that spanned by its total outflowing momentum. -/
def EdgeMomenta : Type := F.𝓔 → ℝ
instance : AddCommGroup F.EdgeMomenta := Pi.addCommGroup
@ -86,7 +86,7 @@ instance : AddCommGroup F.EdgeMomenta := Pi.addCommGroup
instance : Module ℝ F.EdgeMomenta := Pi.module _ _ _
/-- The type which assocaites to each ege a `1`-dimensional vector space.
Corresponding to that spanned by its total inflowing momentum. -/
Corresponding to that spanned by its total inflowing momentum. -/
def VertexMomenta : Type := F.𝓥 → ℝ
instance : AddCommGroup F.VertexMomenta := Pi.addCommGroup
@ -125,7 +125,7 @@ We define various maps into `F.HalfEdgeMomenta`.
In particular, we define a map from `F.EdgeVertexMomenta` to `F.HalfEdgeMomenta`. This
map represents the space orthogonal (with respect to the standard Euclidean inner product)
to the allowed momenta of half-edges (up-to an offset determined by the
external momenta).
external momenta).
The number of loops of a diagram is defined as the number of half-edges minus
the rank of this matrix.
@ -147,7 +147,7 @@ def vertexToHalfEdgeMomenta : F.VertexMomenta →ₗ[ℝ] F.HalfEdgeMomenta wher
map_smul' _ _ := rfl
/-- The linear map from `F.EdgeVertexMomenta` to `F.HalfEdgeMomenta` induced by
`F.edgeToHalfEdgeMomenta` and `F.vertexToHalfEdgeMomenta`. -/
`F.edgeToHalfEdgeMomenta` and `F.vertexToHalfEdgeMomenta`. -/
def edgeVertexToHalfEdgeMomenta : F.EdgeVertexMomenta →ₗ[ℝ] F.HalfEdgeMomenta :=
DirectSum.toModule ℝ (Fin 2) F.HalfEdgeMomenta
(fun i => match i with | 0 => F.edgeToHalfEdgeMomenta | 1 => F.vertexToHalfEdgeMomenta)
@ -163,7 +163,7 @@ allowed momenta.
-/
/-- The submodule of `F.HalfEdgeMomenta` corresponding to the range of
`F.edgeVertexToHalfEdgeMomenta`. -/
`F.edgeVertexToHalfEdgeMomenta`. -/
def orthogHalfEdgeMomenta : Submodule ℝ F.HalfEdgeMomenta :=
LinearMap.range F.edgeVertexToHalfEdgeMomenta

22
HepLean/FlavorPhysics/CKMMatrix/Basic.lean
View file

@ -293,47 +293,47 @@ def VAbs (i j : Fin 3) : Quotient CKMMatrixSetoid → ℝ :=
Quotient.lift (fun V => VAbs' V i j) (VAbs'_equiv i j)
/-- The absolute value of the `ud`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VudAbs := VAbs 0 0
/-- The absolute value of the `us`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VusAbs := VAbs 0 1
/-- The absolute value of the `ub`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VubAbs := VAbs 0 2
/-- The absolute value of the `cd`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VcdAbs := VAbs 1 0
/-- The absolute value of the `cs`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VcsAbs := VAbs 1 1
/-- The absolute value of the `cb`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VcbAbs := VAbs 1 2
/-- The absolute value of the `td`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VtdAbs := VAbs 2 0
/-- The absolute value of the `ts`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VtsAbs := VAbs 2 1
/-- The absolute value of the `tb`th element of a representative of an equivalence class of
CKM matrices. -/
CKM matrices. -/
@[simp]
abbrev VtbAbs := VAbs 2 2
@ -372,7 +372,7 @@ def Rcdcb (V : CKMMatrix) : ℂ := [V]cd / [V]cb
/-- The ratio of the `cd` and `cb` elements of a CKM matrix. -/
scoped[CKMMatrix] notation (name := cd_cb_ratio) "[" V "]cd|cb" => Rcdcb V
lemma Rcdcb_mul_cb {V : CKMMatrix} (h : [V]cb ≠ 0): [V]cd = Rcdcb V * [V]cb := by
lemma Rcdcb_mul_cb {V : CKMMatrix} (h : [V]cb ≠ 0) : [V]cd = Rcdcb V * [V]cb := by
rw [Rcdcb]
exact (div_mul_cancel₀ (V.1 1 0) h).symm
@ -382,7 +382,7 @@ def Rcscb (V : CKMMatrix) : ℂ := [V]cs / [V]cb
/-- The ratio of the `cs` and `cb` elements of a CKM matrix. -/
scoped[CKMMatrix] notation (name := cs_cb_ratio) "[" V "]cs|cb" => Rcscb V
lemma Rcscb_mul_cb {V : CKMMatrix} (h : [V]cb ≠ 0): [V]cs = Rcscb V * [V]cb := by
lemma Rcscb_mul_cb {V : CKMMatrix} (h : [V]cb ≠ 0) : [V]cs = Rcscb V * [V]cb := by
rw [Rcscb]
exact (div_mul_cancel₀ [V]cs h).symm

4
HepLean/FlavorPhysics/CKMMatrix/Invariants.lean
View file

@ -49,8 +49,8 @@ def jarlskogℂ : Quotient CKMMatrixSetoid → ℂ :=
Quotient.lift jarlskogℂCKM jarlskogℂCKM_equiv
/-- An invariant for CKM mtrices corresponding to the square of the absolute values
of the `us`, `ub` and `cb` elements multipled together divied by `(VudAbs V ^ 2 + VusAbs V ^2)` .
-/
of the `us`, `ub` and `cb` elements multipled together divied by `(VudAbs V ^ 2 + VusAbs V ^2)` .
-/
def VusVubVcdSq (V : Quotient CKMMatrixSetoid) : ℝ :=
VusAbs V ^ 2 * VubAbs V ^ 2 * VcbAbs V ^2 / (VudAbs V ^ 2 + VusAbs V ^2)

2
HepLean/FlavorPhysics/CKMMatrix/PhaseFreedom.lean
View file

@ -165,7 +165,7 @@ def FstRowThdColRealCond (U : CKMMatrix) : Prop := [U]ud = VudAbs ⟦U⟧ ∧ [U
there is no phase difference between the `t`th-row and
the cross product of the conjugates of the `u`th and `c`th rows, and the `cd`th and `cs`th
elements are real and related in a set way.
-/
-/
def ubOnePhaseCond (U : CKMMatrix) : Prop :=
[U]ud = 0 ∧ [U]us = 0 ∧ [U]cb = 0 ∧ [U]ub = 1 ∧ [U]t = conj [U]u ×₃ conj [U]c
∧ [U]cd = - VcdAbs ⟦U⟧ ∧ [U]cs = √(1 - VcdAbs ⟦U⟧ ^ 2)

6
HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/Basic.lean
View file

@ -100,8 +100,8 @@ lemma standParamAsMatrix_unitary (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
parameterization of CKM matrices. -/
def standParam (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) : CKMMatrix :=
⟨standParamAsMatrix θ₁₂ θ₁₃ θ₂₃ δ₁₃, by
rw [mem_unitaryGroup_iff']
exact standParamAsMatrix_unitary θ₁₂ θ₁₃ θ₂₃ δ₁₃⟩
rw [mem_unitaryGroup_iff']
exact standParamAsMatrix_unitary θ₁₂ θ₁₃ θ₂₃ δ₁₃⟩
namespace standParam
lemma cross_product_t (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) :
@ -158,7 +158,7 @@ lemma VusVubVcdSq_eq (θ₁₂ θ₁₃ θ₂₃ δ₁₃ : ℝ) (h1 : 0 ≤ Rea
VusVubVcdSq ⟦standParam θ₁₂ θ₁₃ θ₂₃ δ₁₃⟧ =
Real.sin θ₁₂ ^ 2 * Real.cos θ₁₃ ^ 2 * Real.sin θ₁₃ ^ 2 * Real.sin θ₂₃ ^ 2 := by
simp only [VusVubVcdSq, VusAbs, VAbs, VAbs', Fin.isValue, standParam, standParamAsMatrix,
neg_mul, Quotient.lift_mk, cons_val', cons_val_one, head_cons,
neg_mul, Quotient.lift_mk, cons_val', cons_val_one, head_cons,
empty_val', cons_val_fin_one, cons_val_zero, _root_.map_mul, VubAbs, cons_val_two, tail_cons,
VcbAbs, VudAbs, Complex.abs_ofReal]
by_cases hx : Real.cos θ₁₃ ≠ 0

18
HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/StandardParameters.lean
View file

@ -142,17 +142,17 @@ lemma S₂₃_eq_ℂsin_θ₂₃ (V : Quotient CKMMatrixSetoid) : Complex.sin (
(ofReal_sin _).symm.trans (congrArg ofReal (S₂₃_eq_sin_θ₂₃ V))
lemma complexAbs_sin_θ₁₂ (V : Quotient CKMMatrixSetoid) :
Complex.abs (Complex.sin (θ₁₂ V)) = sin (θ₁₂ V):= by
Complex.abs (Complex.sin (θ₁₂ V)) = sin (θ₁₂ V) := by
rw [S₁₂_eq_ℂsin_θ₁₂, Complex.abs_ofReal, ofReal_inj, abs_eq_self]
exact S₁₂_nonneg _
lemma complexAbs_sin_θ₁₃ (V : Quotient CKMMatrixSetoid) :
Complex.abs (Complex.sin (θ₁₃ V)) = sin (θ₁₃ V):= by
Complex.abs (Complex.sin (θ₁₃ V)) = sin (θ₁₃ V) := by
rw [S₁₃_eq_ℂsin_θ₁₃, Complex.abs_ofReal, ofReal_inj, abs_eq_self]
exact S₁₃_nonneg _
lemma complexAbs_sin_θ₂₃ (V : Quotient CKMMatrixSetoid) :
Complex.abs (Complex.sin (θ₂₃ V)) = sin (θ₂₃ V):= by
Complex.abs (Complex.sin (θ₂₃ V)) = sin (θ₂₃ V) := by
rw [S₂₃_eq_ℂsin_θ₂₃, Complex.abs_ofReal, ofReal_inj, abs_eq_self]
exact S₂₃_nonneg _
@ -185,19 +185,19 @@ lemma C₂₃_eq_ℂcos_θ₂₃ (V : Quotient CKMMatrixSetoid) : Complex.cos (
simp [C₂₃]
lemma complexAbs_cos_θ₁₂ (V : Quotient CKMMatrixSetoid) : Complex.abs (Complex.cos (θ₁₂ V)) =
cos (θ₁₂ V):= by
cos (θ₁₂ V) := by
rw [C₁₂_eq_ℂcos_θ₁₂, Complex.abs_ofReal]
simp only [ofReal_inj, abs_eq_self]
exact Real.cos_arcsin_nonneg _
lemma complexAbs_cos_θ₁₃ (V : Quotient CKMMatrixSetoid) : Complex.abs (Complex.cos (θ₁₃ V)) =
cos (θ₁₃ V):= by
cos (θ₁₃ V) := by
rw [C₁₃_eq_ℂcos_θ₁₃, Complex.abs_ofReal]
simp only [ofReal_inj, abs_eq_self]
exact Real.cos_arcsin_nonneg _
lemma complexAbs_cos_θ₂₃ (V : Quotient CKMMatrixSetoid) : Complex.abs (Complex.cos (θ₂₃ V)) =
cos (θ₂₃ V):= by
cos (θ₂₃ V) := by
rw [C₂₃_eq_ℂcos_θ₂₃, Complex.abs_ofReal]
simp only [ofReal_inj, abs_eq_self]
exact Real.cos_arcsin_nonneg _
@ -349,10 +349,10 @@ lemma mulExpδ₁₃_on_param_δ₁₃ (V : CKMMatrix) (δ₁₃ : ℝ) :
lemma mulExpδ₁₃_on_param_eq_zero_iff (V : CKMMatrix) (δ₁₃ : ℝ) :
mulExpδ₁₃ ⟦standParam (θ₁₂ ⟦V⟧) (θ₁₃ ⟦V⟧) (θ₂₃ ⟦V⟧) δ₁₃⟧ = 0 ↔
VudAbs ⟦V⟧ = 0 ∨ VubAbs ⟦V⟧ = 0 ∨ VusAbs ⟦V⟧ = 0 ∨ VcbAbs ⟦V⟧ = 0 ∨ VtbAbs ⟦V⟧ = 0 := by
VudAbs ⟦V⟧ = 0 ∨ VubAbs ⟦V⟧ = 0 ∨ VusAbs ⟦V⟧ = 0 ∨ VcbAbs ⟦V⟧ = 0 ∨ VtbAbs ⟦V⟧ = 0 := by
rw [VudAbs_eq_C₁₂_mul_C₁₃, VubAbs_eq_S₁₃, VusAbs_eq_S₁₂_mul_C₁₃, VcbAbs_eq_S₂₃_mul_C₁₃,
VtbAbs_eq_C₂₃_mul_C₁₃, ← ofReal_inj,
← ofReal_inj, ← ofReal_inj, ← ofReal_inj, ← ofReal_inj]
VtbAbs_eq_C₂₃_mul_C₁₃, ← ofReal_inj,
← ofReal_inj, ← ofReal_inj, ← ofReal_inj, ← ofReal_inj]
simp only [ofReal_mul]
rw [← S₁₃_eq_ℂsin_θ₁₃, ← S₁₂_eq_ℂsin_θ₁₂, ← S₂₃_eq_ℂsin_θ₂₃,
← C₁₃_eq_ℂcos_θ₁₃, ← C₂₃_eq_ℂcos_θ₂₃,← C₁₂_eq_ℂcos_θ₁₂]

2
HepLean/Mathematics/SO3/Basic.lean
View file

@ -147,7 +147,7 @@ lemma det_minus_id (A : SO(3)) : det (A.1 - 1) = 0 := by
calc
det (A.1 - 1) = det (A.1 - A.1 * A.1ᵀ) := by simp [A.2.2]
_ = det A.1 * det (1 - A.1ᵀ) := by rw [← det_mul, mul_sub, mul_one]
_ = det (1 - A.1ᵀ):= by simp [A.2.1]
_ = det (1 - A.1ᵀ) := by simp [A.2.1]
_ = det (1 - A.1ᵀ)ᵀ := by rw [det_transpose]
_ = det (1 - A.1) := by simp
_ = det (- (A.1 - 1)) := by simp

2
HepLean/SpaceTime/LorentzGroup/Basic.lean
View file

@ -36,7 +36,7 @@ open minkowskiMetric in
/-- The Lorentz group is the subset of matrices which preserve the minkowski metric. -/
def LorentzGroup (d : ℕ) : Set (Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ) :=
{Λ : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ |
∀ (x y : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ y⟫ₘ = ⟪x, y⟫ₘ}
∀ (x y : LorentzVector d), ⟪Λ *ᵥ x, Λ *ᵥ y⟫ₘ = ⟪x, y⟫ₘ}
namespace LorentzGroup
/-- Notation for the Lorentz group. -/

2
HepLean/SpaceTime/LorentzGroup/Boosts.lean
View file

@ -145,7 +145,7 @@ lemma toMatrix_in_lorentzGroup (u v : FuturePointing d) : (toMatrix u v) ∈ Lor
smul_eq_mul, LinearMap.neg_apply]
field_simp
rw [u.1.2, v.1.2, minkowskiMetric.symm v.1.1 u, minkowskiMetric.symm u y,
minkowskiMetric.symm v y]
minkowskiMetric.symm v y]
ring
/-- A generalised boost as an element of the Lorentz Group. -/

6
HepLean/SpaceTime/LorentzGroup/Orthochronous.lean
View file

@ -63,7 +63,7 @@ lemma not_orthochronous_iff_le_zero :
/-- The continuous map taking a Lorentz transformation to its `0 0` element. -/
def timeCompCont : C(LorentzGroup d, ℝ) := ⟨fun Λ => timeComp Λ,
Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
Continuous.matrix_elem (continuous_iff_le_induced.mpr fun _ a => a) (Sum.inl 0) (Sum.inl 0)⟩
/-- An auxillary function used in the definition of `orthchroMapReal`. -/
def stepFunction : ℝ → ℝ := fun t =>
@ -72,7 +72,7 @@ def stepFunction : ℝ → ℝ := fun t =>
lemma stepFunction_continuous : Continuous stepFunction := by
apply Continuous.if ?_ continuous_const (Continuous.if ?_ continuous_const continuous_id)
<;> intro a ha
<;> intro a ha
rw [@Set.Iic_def, @frontier_Iic, @Set.mem_singleton_iff] at ha
rw [ha]
simp [neg_lt_self_iff, zero_lt_one, ↓reduceIte]
@ -157,7 +157,7 @@ def orthchroRep : LorentzGroup d →* ℤ₂ where
map_mul' Λ Λ' := by
simp only
by_cases h : IsOrthochronous Λ
<;> by_cases h' : IsOrthochronous Λ'
<;> by_cases h' : IsOrthochronous Λ'
rw [orthchroMap_IsOrthochronous h, orthchroMap_IsOrthochronous h',
orthchroMap_IsOrthochronous (mul_othchron_of_othchron_othchron h h')]
rfl

4
HepLean/SpaceTime/LorentzTensor/Real/Basic.lean
View file

@ -27,7 +27,7 @@ This will relation should be made explicit in the future.
/-! TODO: Generalize to maps into Lorentz tensors. -/
/-- The possible `colors` of an index for a RealLorentzTensor.
There are two possibilities, `up` and `down`. -/
There are two possiblities, `up` and `down`. -/
inductive RealLorentzTensor.Colors where
| up : RealLorentzTensor.Colors
| down : RealLorentzTensor.Colors
@ -361,7 +361,7 @@ def splitIndexValue {T : Marked d X n} :
(indexValueIso d (Equiv.refl _) T.color_eq_elim).trans
indexValueSumEquiv
@[simp]
@[simp]
lemma splitIndexValue_sum {T : Marked d X n} [Fintype X] [DecidableEq X]
(P : T.UnmarkedIndexValue × T.MarkedIndexValue → ℝ) :
∑ i, P (splitIndexValue i) = ∑ j, ∑ k, P (j, k) := by

4
HepLean/SpaceTime/LorentzTensor/Real/Multiplication.lean
View file

@ -209,7 +209,7 @@ lemma mul_unmarkedLorentzAction (T : Marked d X 1) (S : Marked d Y 1)
S.coord (splitIndexValue.symm (k, oneMarkedIndexValue $ colorsIndexDualCast h x)) = _
trans ∑ x, ∑ j, ∑ k, (toTensorRepMat Λ (indexValueSumEquiv i).1 j *
T.coord (splitIndexValue.symm (j, oneMarkedIndexValue x)))*
toTensorRepMat Λ (indexValueSumEquiv i).2 k *
toTensorRepMat Λ (indexValueSumEquiv i).2 k *
S.coord (splitIndexValue.symm (k, oneMarkedIndexValue $ colorsIndexDualCast h x))
· apply Finset.sum_congr rfl (fun x _ => ?_)
rw [Finset.sum_mul_sum ]
@ -219,7 +219,7 @@ lemma mul_unmarkedLorentzAction (T : Marked d X 1) (S : Marked d Y 1)
rw [Finset.sum_comm]
trans ∑ j, ∑ k, ∑ x, (toTensorRepMat Λ (indexValueSumEquiv i).1 j *
T.coord (splitIndexValue.symm (j, oneMarkedIndexValue x)))*
toTensorRepMat Λ (indexValueSumEquiv i).2 k *
toTensorRepMat Λ (indexValueSumEquiv i).2 k *
S.coord (splitIndexValue.symm (k, oneMarkedIndexValue $ colorsIndexDualCast h x))
· exact Finset.sum_congr rfl (fun j _ => Finset.sum_comm)
trans ∑ j, ∑ k,

6
HepLean/SpaceTime/LorentzVector/NormOne.lean
View file

@ -277,9 +277,9 @@ lemma metric_continuous (u : LorentzVector d) :
(continuous_apply (Sum.inl 0))
(Continuous.comp' continuous_subtype_val continuous_subtype_val)
· refine Continuous.comp' continuous_neg $ Continuous.inner
(Continuous.comp' (Pi.continuous_precomp Sum.inr) continuous_const)
(Continuous.comp' (Pi.continuous_precomp Sum.inr) (Continuous.comp'
continuous_subtype_val continuous_subtype_val))
(Continuous.comp' (Pi.continuous_precomp Sum.inr) continuous_const)
(Continuous.comp' (Pi.continuous_precomp Sum.inr) (Continuous.comp'
continuous_subtype_val continuous_subtype_val))
end FuturePointing

2
HepLean/SpaceTime/MinkowskiMetric.lean
View file

@ -328,7 +328,7 @@ lemma on_basis (μ ν : Fin 1 ⊕ Fin d) : ⟪e μ, e ν⟫ₘ = η μ ν := by
· simp [h, LieAlgebra.Orthogonal.indefiniteDiagonal, minkowskiMatrix]
exact fun a => False.elim (h (id (Eq.symm a)))
lemma matrix_apply_stdBasis (ν μ : Fin 1 ⊕ Fin d):
lemma matrix_apply_stdBasis (ν μ : Fin 1 ⊕ Fin d) :
Λ ν μ = η ν ν * ⟪e ν, Λ *ᵥ e μ⟫ₘ := by
rw [on_basis_mulVec, ← mul_assoc]
have h1 : η ν ν * η ν ν = 1 := by

6
HepLean/SpaceTime/SL2C/Basic.lean
View file

@ -34,7 +34,7 @@ we can define a representation a representation of `SL(2, ℂ)` on spacetime.
-/
/-- Given an element `M ∈ SL(2, ℂ)` the linear map from `selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)` to
itself defined by `A ↦ M * A * Mᴴ`. -/
itself defined by `A ↦ M * A * Mᴴ`. -/
@[simps!]
def toLinearMapSelfAdjointMatrix (M : SL(2, ℂ)) :
selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ) →ₗ[ℝ] selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ) where
@ -51,7 +51,7 @@ def toLinearMapSelfAdjointMatrix (M : SL(2, ℂ)) :
RingHom.id_apply]
/-- The representation of `SL(2, ℂ)` on `selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)` given by
`M A ↦ M * A * Mᴴ`. -/
`M A ↦ M * A * Mᴴ`. -/
@[simps!]
def repSelfAdjointMatrix : Representation ℝ SL(2, ℂ) $ selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ) where
toFun := toLinearMapSelfAdjointMatrix
@ -103,7 +103,7 @@ lemma iff_det_selfAdjoint (Λ : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ)
@[simps!]
def toLorentzGroupElem (M : SL(2, ℂ)) : LorentzGroup 3 :=
⟨LinearMap.toMatrix LorentzVector.stdBasis LorentzVector.stdBasis (repLorentzVector M),
by simp [repLorentzVector, iff_det_selfAdjoint]⟩
by simp [repLorentzVector, iff_det_selfAdjoint]⟩
/-- The group homomorphism from ` SL(2, ℂ)` to the Lorentz group `𝓛`. -/
@[simps!]

4
HepLean/StandardModel/HiggsBoson/GaugeAction.lean
View file

@ -76,7 +76,7 @@ def unitToLinear : unitary (HiggsVec →L[ℂ] HiggsVec) →* HiggsVec →ₗ[
/-- The representation of the gauge group acting on `higgsVec`. -/
@[simps!]
def rep : Representation ℂ GaugeGroup HiggsVec :=
unitToLinear.comp (unitaryToLin.comp higgsRepUnitary)
unitToLinear.comp (unitaryToLin.comp higgsRepUnitary)
lemma higgsRepUnitary_mul (g : GaugeGroup) (φ : HiggsVec) :
(higgsRepUnitary g).1 *ᵥ φ = g.2.2 ^ 3 • (g.2.1.1 *ᵥ φ) := by
@ -138,7 +138,7 @@ lemma rotateGuageGroup_apply {φ : HiggsVec} (hφ : φ ≠ 0) :
rep (rotateGuageGroup hφ) φ = ![0, ofReal ‖φ‖] := by
rw [rep_apply]
simp only [rotateGuageGroup, rotateMatrix, one_pow, one_smul,
Nat.succ_eq_add_one, Nat.reduceAdd, ofReal_eq_coe]
Nat.succ_eq_add_one, Nat.reduceAdd, ofReal_eq_coe]
ext i
fin_cases i
· simp only [mulVec, Fin.zero_eta, Fin.isValue, cons_val', empty_val', cons_val_fin_one,

3
HepLean/StandardModel/HiggsBoson/PointwiseInnerProd.lean
View file

@ -55,8 +55,7 @@ lemma innerProd_left_zero (φ : HiggsField) : ⟪0, φ⟫_H = 0 := by
lemma innerProd_right_zero (φ : HiggsField) : ⟪φ, 0⟫_H = 0 := by
funext x
simp [innerProd]
example (x : ℝ): RCLike.ofReal x = ofReal' x := by
rfl
lemma innerProd_expand (φ1 φ2 : HiggsField) :
⟪φ1, φ2⟫_H = fun x => equivRealProdCLM.symm (((φ1 x 0).re * (φ2 x 0).re
+ (φ1 x 1).re * (φ2 x 1).re+ (φ1 x 0).im * (φ2 x 0).im + (φ1 x 1).im * (φ2 x 1).im),

2
HepLean/StandardModel/Representations.lean
View file

@ -32,7 +32,7 @@ noncomputable def repU1Map (g : unitary ℂ) : unitaryGroup (Fin 2) ℂ :=
simp only [one_pow, one_smul]⟩
/-- The 2d representation of U(1) with charge 3 as a homomorphism
from U(1) to `unitaryGroup (Fin 2) ℂ`. -/
from U(1) to `unitaryGroup (Fin 2) ℂ`. -/
@[simps!]
noncomputable def repU1 : unitary ℂ →* unitaryGroup (Fin 2) ℂ where
toFun g := repU1Map g

43
scripts/hepLean_style_lint.lean
View file

@ -5,6 +5,7 @@ Authors: Joseph Tooby-Smith
-/
import Lean
import Mathlib.Tactic.Linter.TextBased
import Batteries.Data.Array.Merge
/-!
# HepLean style linter
@ -60,7 +61,17 @@ def substringLinter (s : String) : HepLeanTextLinter := fun lines ↦ Id.run do
let col := match k with
| none => 1
| some k => String.offsetOfPos l k.stopPos
some (s!" Found instance of substring {s}.", lno, col)
some (s!" Found instance of substring `{s}`.", lno, col)
else none)
errors.toArray
/-- Number of space at new line must be even. -/
def numInitialSpacesEven : HepLeanTextLinter := fun lines ↦ Id.run do
let enumLines := (lines.toList.enumFrom 1)
let errors := enumLines.filterMap (fun (lno, l) ↦
let numSpaces := (l.takeWhile (· == ' ')).length
if numSpaces % 2 != 0 then
some (s!"Number of initial spaces is not even.", lno, 1)
else none)
errors.toArray
@ -78,18 +89,18 @@ def printErrors (errors : Array HepLeanErrorContext) : IO Unit := do
for e in errors do
IO.println (s!"error: {e.path}:{e.lineNumber}:{e.columnNumber}: {e.error}")
def hepLeanLintFile (path : FilePath) : IO Bool := do
def hepLeanLintFile (path : FilePath) : IO (Array HepLeanErrorContext) := do
let lines ← IO.FS.lines path
let allOutput := (Array.map (fun lint ↦
(Array.map (fun (e, n, c) ↦ HepLeanErrorContext.mk e n c path)) (lint lines)))
#[doubleEmptyLineLinter, doubleSpaceLinter, substringLinter ".-/", substringLinter " )",
#[doubleEmptyLineLinter, doubleSpaceLinter, numInitialSpacesEven,
substringLinter ".-/", substringLinter " )",
substringLinter "( ", substringLinter "=by", substringLinter " def ",
substringLinter "/-- We ", substringLinter "[ ", substringLinter " ]", substringLinter " ,"
, substringLinter "by exact ",
substringLinter "⟨ ", substringLinter " ⟩"]
substringLinter "⟨ ", substringLinter " ⟩", substringLinter "):"]
let errors := allOutput.flatten
printErrors errors
return errors.size > 0
return errors
def main (_ : List String) : IO UInt32 := do
initSearchPath (← findSysroot)
@ -99,13 +110,19 @@ def main (_ : List String) : IO UInt32 := do
unless (← mFile.pathExists) do
throw <| IO.userError s!"object file '{mFile}' of module {imp.module} does not exist"
let (hepLeanMod, _) ← readModuleData mFile
let mut warned := false
for imp in hepLeanMod.imports do
if imp.module == `Init then continue
let filePath := (mkFilePath (imp.module.toString.split (· == '.'))).addExtension "lean"
if ← hepLeanLintFile filePath then
warned := true
if warned then
let filePaths := hepLeanMod.imports.filterMap (fun imp ↦
if imp.module == `Init then
none
else
some ((mkFilePath (imp.module.toString.split (· == '.'))).addExtension "lean"))
let errors := (← filePaths.mapM hepLeanLintFile).flatten
let errorMessagesPresent := (errors.map (fun e => e.error)).sortDedup
for eM in errorMessagesPresent do
IO.println s!"\n\nError: {eM}"
for e in errors do
if e.error == eM then
IO.println s!"{e.path}:{e.lineNumber}:{e.columnNumber}: {e.error}"
if errors.size > 0 then
throw <| IO.userError s!"Errors found."
else
IO.println "No linting issues found."