refactor: Lint

This commit is contained in:
jstoobysmith 2024-04-17 14:49:59 -04:00
parent fafcba9bf1
commit 61f61c3e79
4 changed files with 39 additions and 31 deletions

View file

@ -51,7 +51,7 @@ lemma charges_eq_toSpecies_eq (S T : (SMCharges n).charges) :
apply Iff.intro
intro h
rw [h]
simp
simp only [forall_const]
intro h
apply toSpeciesEquiv.injective
funext i
@ -108,7 +108,8 @@ def accGrav : (SMCharges n).charges →ₗ[] where
lemma accGrav_ext {S T : (SMCharges n).charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accGrav S = accGrav T := by
simp
simp only [accGrav, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
AddHom.coe_mk]
repeat erw [Finset.sum_add_distrib]
repeat erw [← Finset.mul_sum]
repeat erw [hj]
@ -137,7 +138,8 @@ def accSU2 : (SMCharges n).charges →ₗ[] where
lemma accSU2_ext {S T : (SMCharges n).charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accSU2 S = accSU2 T := by
simp
simp only [accSU2, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
AddHom.coe_mk]
repeat erw [Finset.sum_add_distrib]
repeat erw [← Finset.mul_sum]
repeat erw [hj]
@ -166,7 +168,8 @@ def accSU3 : (SMCharges n).charges →ₗ[] where
lemma accSU3_ext {S T : (SMCharges n).charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accSU3 S = accSU3 T := by
simp
simp only [accSU3, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
AddHom.coe_mk]
repeat erw [Finset.sum_add_distrib]
repeat erw [← Finset.mul_sum]
repeat erw [hj]
@ -196,7 +199,8 @@ def accYY : (SMCharges n).charges →ₗ[] where
lemma accYY_ext {S T : (SMCharges n).charges}
(hj : ∀ (j : Fin 5), ∑ i, (toSpecies j) S i = ∑ i, (toSpecies j) T i) :
accYY S = accYY T := by
simp
simp only [accYY, SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, LinearMap.coe_mk,
AddHom.coe_mk]
repeat erw [Finset.sum_add_distrib]
repeat erw [← Finset.mul_sum]
repeat erw [hj]
@ -224,10 +228,11 @@ def quadBiLin : BiLinearSymm (SMCharges n).charges where
apply Fintype.sum_congr
intro i
repeat erw [map_add]
simp
simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue, neg_mul,
one_mul]
ring
swap' S T := by
simp
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, neg_mul, one_mul]
apply Fintype.sum_congr
intro i
ring
@ -274,15 +279,15 @@ def cubeTriLin : TriLinearSymm (SMCharges n).charges where
apply Fintype.sum_congr
intro i
repeat erw [map_add]
simp
simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue]
ring
swap₁' S T L := by
simp
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
apply Fintype.sum_congr
intro i
ring
swap₂' S T L := by
simp
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
apply Fintype.sum_congr
intro i
ring

View file

@ -66,7 +66,7 @@ def speciesEmbed (m n : ) :
0
map_add' S T := by
funext i
simp
simp only [SMSpecies_numberCharges, ACCSystemCharges.chargesAddCommMonoid_add]
by_cases hi : i.val < m
erw [dif_pos hi, dif_pos hi, dif_pos hi]
erw [dif_neg hi, dif_neg hi, dif_neg hi]

View file

@ -6,7 +6,6 @@ Authors: Joseph Tooby-Smith
import HepLean.AnomalyCancellation.SM.Basic
import HepLean.AnomalyCancellation.SM.NoGrav.Basic
import HepLean.AnomalyCancellation.SM.NoGrav.One.LinearParameterization
universe v u
/-!
# Lemmas for 1 family SM Accs
@ -16,6 +15,7 @@ https://arxiv.org/abs/1907.00514
That eveery solution to the ACCs without gravity satifies for free the gravitational anomaly.
-/
universe v u
namespace SM
namespace SMNoGrav
namespace One

View file

@ -9,8 +9,6 @@ import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.NumberTheory.FLT.Basic
import Mathlib.Algebra.QuadraticDiscriminant
universe v u
/-!
# Parameterizations for solutions to the linear ACCs for 1 family
@ -22,7 +20,7 @@ These parameterizations are based on:
https://arxiv.org/abs/1907.00514
-/
universe v u
namespace SM
namespace SMNoGrav
namespace One
@ -43,7 +41,8 @@ structure linearParameters where
namespace linearParameters
@[ext]
lemma ext {S T : linearParameters} (hQ : S.Q' = T.Q') (hY : S.Y = T.Y) (hE : S.E' = T.E') : S = T := by
lemma ext {S T : linearParameters} (hQ : S.Q' = T.Q') (hY : S.Y = T.Y) (hE : S.E' = T.E') :
S = T := by
cases' S
simp_all only
@ -57,7 +56,8 @@ def asCharges (S : linearParameters) : (SMNoGrav 1).charges := fun i =>
| (3: Fin 5) => - 3 * S.Q'
| (4 : Fin 5) => S.E'
lemma speciesVal (S : linearParameters) : (toSpecies i) S.asCharges (0 : Fin 1) = S.asCharges i := by
lemma speciesVal (S : linearParameters) :
(toSpecies i) S.asCharges (0 : Fin 1) = S.asCharges i := by
match i with
| 0 => rfl
| 1 => rfl
@ -76,7 +76,7 @@ def asLinear (S : linearParameters) : (SMNoGrav 1).LinSols :=
simp only [accSU3, SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero,
Fin.isValue, Finset.sum_singleton, LinearMap.coe_mk, AddHom.coe_mk]
repeat erw [speciesVal]
simp
simp only [asCharges, neg_add_rev]
ring)
lemma asLinear_val (S : linearParameters) : S.asLinear.val = S.asCharges := by
@ -92,7 +92,7 @@ lemma cubic (S : linearParameters) :
simp only [SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
Finset.sum_singleton]
repeat erw [speciesVal]
simp
simp only [asCharges, neg_add_rev, neg_mul, mul_neg, neg_neg]
ring
lemma cubic_zero_Q'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
@ -129,13 +129,13 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
repeat erw [speciesVal]
simp only [Fin.isValue]
repeat erw [speciesVal]
simp
simp only [asCharges, neg_add_rev]
ring
simp only [toSpecies_apply]
repeat erw [speciesVal]
rfl
right_inv S := by
simp
simp only [Fin.isValue, toSpecies_apply]
apply ACCSystemLinear.LinSols.ext
rw [charges_eq_toSpecies_eq]
intro i
@ -167,7 +167,7 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
/-- The bijection between the linear parameters and `(SMNoGrav 1).LinSols` in the special
case when Q and E are both not zero. -/
def bijectionQEZero : {S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0} ≃
{S : (SMNoGrav 1).LinSols // Q S.val (0 : Fin 1) ≠ 0 ∧ E S.val (0 : Fin 1) ≠ 0} where
{S : (SMNoGrav 1).LinSols // Q S.val (0 : Fin 1) ≠ 0 ∧ E S.val (0 : Fin 1) ≠ 0} where
toFun S := ⟨bijection S, S.2⟩
invFun S := ⟨bijection.symm S, S.2⟩
left_inv S := by
@ -183,7 +183,7 @@ lemma grav (S : linearParameters) :
simp only [SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
Finset.sum_singleton, LinearMap.coe_mk, AddHom.coe_mk]
repeat erw [speciesVal]
simp
simp only [asCharges, neg_add_rev, neg_mul, mul_neg]
ring_nf
rw [add_comm, add_eq_zero_iff_eq_neg]
simp
@ -217,7 +217,8 @@ def toLinearParameters (S : linearParametersQENeqZero) :
⟨⟨S.x, 3 * S.x * (S.v - S.w) / (S.v + S.w), - 6 * S.x / (S.v + S.w)⟩,
by
apply And.intro S.hx
simp
simp only [neg_mul, ne_eq, div_eq_zero_iff, neg_eq_zero, mul_eq_zero, OfNat.ofNat_ne_zero,
false_or]
rw [not_or]
exact And.intro S.hx S.hvw⟩
@ -228,11 +229,11 @@ def tolinearParametersQNeqZero (S : {S : linearParameters // S.Q' ≠ 0 ∧ S.
linearParametersQENeqZero :=
⟨S.1.Q', - (3 * S.1.Q' + S.1.Y) / S.1.E', - (3 * S.1.Q' - S.1.Y)/ S.1.E', S.2.1,
by
simp
simp only [ne_eq, neg_add_rev, neg_sub]
field_simp
rw [not_or]
ring_nf
simp
simp only [neg_eq_zero, mul_eq_zero, OfNat.ofNat_ne_zero, or_false]
exact S.2⟩
/-- A bijection between the type `linearParametersQENeqZero` and linear parameters
@ -246,10 +247,11 @@ def bijectionLinearParameters :
have hvw := S.hvw
have hQ := S.hx
apply linearParametersQENeqZero.ext
simp
simp only [tolinearParametersQNeqZero_x, toLinearParameters_coe_Q']
field_simp
ring
simp
simp only [tolinearParametersQNeqZero_w, toLinearParameters_coe_Y, toLinearParameters_coe_Q',
toLinearParameters_coe_E']
field_simp
ring
right_inv S := by
@ -257,7 +259,7 @@ def bijectionLinearParameters :
have hQ := S.2.1
have hE := S.2.2
apply linearParameters.ext
simp
simp only [ne_eq, toLinearParameters_coe_Q', tolinearParametersQNeqZero_x]
field_simp
ring_nf
field_simp [hQ, hE]
@ -275,7 +277,8 @@ def bijection : linearParametersQENeqZero ≃
lemma cubic (S : linearParametersQENeqZero) :
accCube (bijection S).1.val = 0 ↔ S.v ^ 3 + S.w ^ 3 = -1 := by
erw [linearParameters.cubic]
simp
simp only [ne_eq, bijectionLinearParameters_apply_coe_Q', neg_mul,
bijectionLinearParameters_apply_coe_Y, div_pow, bijectionLinearParameters_apply_coe_E']
have hvw := S.hvw
have hQ := S.hx
field_simp
@ -365,7 +368,7 @@ lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1
have h' := cube_w_v S h
cases' h' with h h
rw [h.1, h.2]
simp
simp only [add_zero]
rw [h.1, h.2]
simp