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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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20
HepLean/FeynmanDiagrams/Momentum.lean
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@ -45,8 +45,8 @@ 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. -/
def HalfEdgeMomenta : Type := F.𝓱𝓔 → ℝ
Corresponding to that spanned by its momentum. -/
def HalfEdgeMomenta : Type := F.𝓱𝓔 → ℝ
instance : AddCommGroup F.HalfEdgeMomenta := Pi.addCommGroup
@ -54,14 +54,14 @@ instance : Module ℝ F.HalfEdgeMomenta := Pi.module _ _ _
/-- An auxillary function used to define the Euclidean inner product on `F.HalfEdgeMomenta`. -/
def euclidInnerAux (x : F.HalfEdgeMomenta) : F.HalfEdgeMomenta →ₗ[ℝ] ℝ where
toFun y := ∑ i, (x i) * (y i)
toFun y := ∑ i, (x i) * (y i)
map_add' z y :=
show (∑ i, (x i) * (z i + y i)) = (∑ i, x i * z i) + ∑ i, x i * (y i) by
simp only [mul_add, Finset.sum_add_distrib]
map_smul' c y :=
show (∑ i, x i * (c * y i)) = c * ∑ i, x i * y i by
rw [Finset.mul_sum]
refine Finset.sum_congr rfl (fun _ _ => by ring)
refine Finset.sum_congr rfl (fun _ _ => by ring)
lemma euclidInnerAux_symm (x y : F.HalfEdgeMomenta) :
F.euclidInnerAux x y = F.euclidInnerAux y x := Finset.sum_congr rfl (fun _ _ => by ring)
@ -70,15 +70,15 @@ lemma euclidInnerAux_symm (x y : F.HalfEdgeMomenta) :
def euclidInner : F.HalfEdgeMomenta →ₗ[ℝ] F.HalfEdgeMomenta →ₗ[ℝ] ℝ where
toFun x := F.euclidInnerAux x
map_add' x y := by
refine LinearMap.ext (fun z => ?_)
refine LinearMap.ext (fun z => ?_)
simp only [euclidInnerAux_symm, map_add, LinearMap.add_apply]
map_smul' c x := by
refine LinearMap.ext (fun z => ?_)
refine LinearMap.ext (fun z => ?_)
simp only [euclidInnerAux_symm, LinearMapClass.map_smul, smul_eq_mul, RingHom.id_apply,
LinearMap.smul_apply]
/-- The type which assocaites to each ege 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
@ -96,8 +96,8 @@ instance : Module ℝ F.VertexMomenta := Pi.module _ _ _
/-- The map from `Fin 2` to `Type` landing on `EdgeMomenta` and `VertexMomenta`. -/
def EdgeVertexMomentaMap : Fin 2 → Type := fun i =>
match i with
| 0 => F.EdgeMomenta
| 1 => F.VertexMomenta
| 0 => F.EdgeMomenta
| 1 => F.VertexMomenta
instance (i : Fin 2) : AddCommGroup (EdgeVertexMomentaMap F i) :=
match i with