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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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24
HepLean/AnomalyCancellation/MSSMNu/Permutations.lean
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@ -17,7 +17,7 @@ and its action on the MSSM.
universe v u
open Nat
open Finset
open Finset
namespace MSSM
@ -30,7 +30,7 @@ open BigOperators
def PermGroup := Fin 6 → Equiv.Perm (Fin 3)
@[simp]
instance : Group PermGroup := Pi.group
instance : Group PermGroup := Pi.group
/-- The image of an element of `permGroup` under the representation on charges. -/
@[simps!]
@ -65,7 +65,7 @@ def repCharges : Representation ℚ PermGroup (MSSMCharges).Charges where
apply LinearMap.ext
intro S
rw [charges_eq_toSpecies_eq]
refine And.intro ?_ $ Prod.mk.inj_iff.mp rfl
refine And.intro ?_ $ Prod.mk.inj_iff.mp rfl
intro i
simp only [ Pi.mul_apply, Pi.inv_apply, Equiv.Perm.coe_mul, LinearMap.mul_apply]
rw [chargeMap_toSpecies, chargeMap_toSpecies]
@ -76,7 +76,7 @@ def repCharges : Representation ℚ PermGroup (MSSMCharges).Charges where
apply LinearMap.ext
intro S
rw [charges_eq_toSpecies_eq]
refine And.intro ?_ $ Prod.mk.inj_iff.mp rfl
refine And.intro ?_ $ Prod.mk.inj_iff.mp rfl
intro i
erw [toSMSpecies_toSpecies_inv]
rfl
@ -91,46 +91,46 @@ lemma toSpecies_sum_invariant (m : ℕ) (f : PermGroup) (S : MSSMCharges.Charges
rw [repCharges_toSMSpecies]
exact Equiv.sum_comp (f⁻¹ j) ((fun a => a ^ m) ∘ (toSMSpecies j) S)
lemma Hd_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma Hd_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
Hd (repCharges f S) = Hd S := rfl
lemma Hu_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma Hu_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
Hu (repCharges f S) = Hu S := rfl
lemma accGrav_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma accGrav_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
accGrav (repCharges f S) = accGrav S :=
accGrav_ext
(by simpa using toSpecies_sum_invariant 1 f S)
(Hd_invariant f S)
(Hu_invariant f S)
lemma accSU2_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma accSU2_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
accSU2 (repCharges f S) = accSU2 S :=
accSU2_ext
(by simpa using toSpecies_sum_invariant 1 f S)
(Hd_invariant f S)
(Hu_invariant f S)
lemma accSU3_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma accSU3_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
accSU3 (repCharges f S) = accSU3 S :=
accSU3_ext
(by simpa using toSpecies_sum_invariant 1 f S)
lemma accYY_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma accYY_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
accYY (repCharges f S) = accYY S :=
accYY_ext
(by simpa using toSpecies_sum_invariant 1 f S)
(Hd_invariant f S)
(Hu_invariant f S)
lemma accQuad_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma accQuad_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
accQuad (repCharges f S) = accQuad S :=
accQuad_ext
(toSpecies_sum_invariant 2 f S)
(Hd_invariant f S)
(Hu_invariant f S)
lemma accCube_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
lemma accCube_invariant (f : PermGroup) (S : MSSMCharges.Charges) :
accCube (repCharges f S) = accCube S :=
accCube_ext
(fun j => toSpecies_sum_invariant 3 f S j)