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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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8
HepLean/AnomalyCancellation/SM/NoGrav/Basic.lean
View file

@ -36,17 +36,17 @@ namespace SMNoGrav
variable {n : ℕ}
lemma SU2Sol (S : (SMNoGrav n).LinSols) : accSU2 S.val = 0 := by
lemma SU2Sol (S : (SMNoGrav n).LinSols) : accSU2 S.val = 0 := by
have hS := S.linearSol
simp at hS
exact hS 0
lemma SU3Sol (S : (SMNoGrav n).LinSols) : accSU3 S.val = 0 := by
lemma SU3Sol (S : (SMNoGrav n).LinSols) : accSU3 S.val = 0 := by
have hS := S.linearSol
simp at hS
exact hS 1
lemma cubeSol (S : (SMNoGrav n).Sols) : accCube S.val = 0 := by
lemma cubeSol (S : (SMNoGrav n).Sols) : accCube S.val = 0 := by
exact S.cubicSol
/-- An element of `charges` which satisfies the linear ACCs
@ -84,7 +84,7 @@ def chargeToAF (S : (SMNoGrav n).Charges) (hSU2 : accSU2 S = 0) (hSU3 : accSU3 S
(hc : accCube S = 0) : (SMNoGrav n).Sols :=
quadToAF (chargeToQuad S hSU2 hSU3) hc
/-- An element of `AnomalyFreeLinear` which satisfies the quadratic and cubic ACCs
/-- An element of `AnomalyFreeLinear` which satisfies the quadratic and cubic ACCs
gives us a element of `AnomalyFree`. -/
def linearToAF (S : (SMNoGrav n).LinSols)
(hc : accCube S.val = 0) : (SMNoGrav n).Sols :=

10
HepLean/AnomalyCancellation/SM/NoGrav/One/Lemmas.lean
View file

@ -25,11 +25,11 @@ open SMACCs
open BigOperators
lemma E_zero_iff_Q_zero {S : (SMNoGrav 1).Sols} : Q S.val (0 : Fin 1) = 0 ↔
E S.val (0 : Fin 1) = 0 := by
E S.val (0 : Fin 1) = 0 := by
let S' := linearParameters.bijection.symm S.1.1
have hC := cubeSol S
have hS' := congrArg (fun S => S.val) (linearParameters.bijection.right_inv S.1.1)
change S'.asCharges = S.val at hS'
change S'.asCharges = S.val at hS'
rw [← hS'] at hC
apply Iff.intro
intro hQ
@ -37,7 +37,7 @@ lemma E_zero_iff_Q_zero {S : (SMNoGrav 1).Sols} : Q S.val (0 : Fin 1) = 0 ↔
intro hE
exact S'.cubic_zero_E'_zero hC hE
lemma accGrav_Q_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) = 0) :
lemma accGrav_Q_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) = 0) :
accGrav S.val = 0 := by
rw [accGrav]
simp only [SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
@ -59,12 +59,12 @@ lemma accGrav_Q_neq_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) ≠ 0
have hC := cubeSol S
have hS' := congrArg (fun S => S.val.val)
(linearParametersQENeqZero.bijection.right_inv ⟨S.1.1, And.intro hQ hE⟩)
change _ = S.val at hS'
change _ = S.val at hS'
rw [← hS'] at hC
rw [← hS']
exact S'.grav_of_cubic hC FLTThree
/-- Any solution to the ACCs without gravity satisfies the gravitational ACC. -/
/-- Any solution to the ACCs without gravity satisfies the gravitational ACC. -/
theorem accGravSatisfied {S : (SMNoGrav 1).Sols} (FLTThree : FermatLastTheoremWith ℚ 3) :
accGrav S.val = 0 := by
by_cases hQ : Q S.val (0 : Fin 1)= 0

18
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
View file

@ -198,15 +198,15 @@ namespace linearParametersQENeqZero
@[ext]
lemma ext {S T : linearParametersQENeqZero} (hx : S.x = T.x) (hv : S.v = T.v)
(hw : S.w = T.w) : S = T := by
(hw : S.w = T.w) : S = T := by
cases' S
simp_all only
/-- A map from `linearParametersQENeqZero` to `linearParameters`. -/
@[simps!]
def toLinearParameters (S : linearParametersQENeqZero) :
{S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0} :=
⟨⟨S.x, 3 * S.x * (S.v - S.w) / (S.v + S.w), - 6 * S.x / (S.v + S.w)⟩,
{S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0} :=
⟨⟨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 only [neg_mul, ne_eq, div_eq_zero_iff, neg_eq_zero, mul_eq_zero, OfNat.ofNat_ne_zero,
@ -217,9 +217,9 @@ def toLinearParameters (S : linearParametersQENeqZero) :
/-- A map from `linearParameters` to `linearParametersQENeqZero` in the special case when
`Q'` and `E'` of the linear parameters are non-zero. -/
@[simps!]
def tolinearParametersQNeqZero (S : {S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0}) :
def tolinearParametersQNeqZero (S : {S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0}) :
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,
⟨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 only [ne_eq, neg_add_rev, neg_sub]
field_simp
@ -231,7 +231,7 @@ def tolinearParametersQNeqZero (S : {S : linearParameters // S.Q' ≠ 0 ∧ S.
with `Q'` and `E'` non-zero. -/
@[simps!]
def bijectionLinearParameters :
linearParametersQENeqZero ≃ {S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0} where
linearParametersQENeqZero ≃ {S : linearParameters // S.Q' ≠ 0 ∧ S.E' ≠ 0} where
toFun := toLinearParameters
invFun := tolinearParametersQNeqZero
left_inv S := by
@ -260,7 +260,7 @@ def bijectionLinearParameters :
/-- The bijection between `linearParametersQENeqZero` and `LinSols` with `Q` and `E` non-zero. -/
def bijection : linearParametersQENeqZero ≃
{S : (SMNoGrav 1).LinSols // Q S.val (0 : Fin 1) ≠ 0 ∧ E S.val (0 : Fin 1) ≠ 0} :=
{S : (SMNoGrav 1).LinSols // Q S.val (0 : Fin 1) ≠ 0 ∧ E S.val (0 : Fin 1) ≠ 0} :=
bijectionLinearParameters.trans (linearParameters.bijectionQEZero)
lemma cubic (S : linearParametersQENeqZero) :
@ -297,7 +297,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
have h' : (S.w + 1) * (1 * S.w * S.w + (-1) * S.w + 1) = 0 := by
ring_nf
exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
have h'' : (1 * S.w * S.w + (-1) * S.w + 1) ≠ 0 := by
have h'' : (1 * S.w * S.w + (-1) * S.w + 1) ≠ 0 := by
refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.w
intro s
by_contra hn
@ -315,7 +315,7 @@ lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.v
have h' : (S.v + 1) * (1 * S.v * S.v + (-1) * S.v + 1) = 0 := by
ring_nf
exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
have h'' : (1 * S.v * S.v + (-1) * S.v + 1) ≠ 0 := by
have h'' : (1 * S.v * S.v + (-1) * S.v + 1) ≠ 0 := by
refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.v
intro s
by_contra hn