refactor: Lint
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6 changed files with 8 additions and 12 deletions
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@ -162,6 +162,5 @@ theorem special_case {S : (PureU1 (2 * n.succ.succ + 1)).Sols}
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have ht := special_case_lineInCubic_perm h
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exact lineInCubicPerm_zero ht
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end Odd
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end PureU1
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@ -298,7 +298,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
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ring_nf
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exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
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have h'' : (1 * (S.w * S.w) + (-1) * S.w + 1) ≠ 0 := by
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refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.w
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refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.w
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intro s
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by_contra hn
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have h : s ^ 2 < 0 := by
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@ -59,19 +59,18 @@ variable (P : PreFeynmanRule)
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/-- The functor from `Over (P.HalfEdgeLabel × P.EdgeLabel × P.VertexLabel)`
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to `Over (P.VertexLabel)` induced by projections on products. -/
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@[simps!]
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def toVertex {𝓔 𝓥 : Type} : Over (P.HalfEdgeLabel × 𝓔 × 𝓥) ⥤ Over 𝓥 :=
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Over.map <| Prod.snd ∘ Prod.snd
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/-- The functor from `Over (P.HalfEdgeLabel × P.EdgeLabel × P.VertexLabel)`
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to `Over (P.EdgeLabel)` induced by projections on products. -/
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@[simps!]
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@[simps! obj_left obj_hom map_left map_right]
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def toEdge {𝓔 𝓥 : Type} : Over (P.HalfEdgeLabel × 𝓔 × 𝓥) ⥤ Over 𝓔 :=
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Over.map <| Prod.fst ∘ Prod.snd
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/-- The functor from `Over (P.HalfEdgeLabel × P.EdgeLabel × P.VertexLabel)`
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to `Over (P.HalfEdgeLabel)` induced by projections on products. -/
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@[simps!]
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@[simps! obj_left obj_hom map_left map_right]
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def toHalfEdge {𝓔 𝓥 : Type} : Over (P.HalfEdgeLabel × 𝓔 × 𝓥) ⥤ Over P.HalfEdgeLabel :=
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Over.map Prod.fst
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@ -477,7 +476,7 @@ def edgeVertexEquiv {F G : FeynmanDiagram P} (𝓔 : F.𝓔 ≃ G.𝓔) (𝓥 :
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right_inv := by aesop_cat
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/-- The functor of over-categories generated by `edgeVertexMap`. -/
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@[simps!]
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@[simps! obj_left obj_hom map_left map_right]
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def edgeVertexFunc {F G : FeynmanDiagram P} (𝓔 : F.𝓔 ⟶ G.𝓔) (𝓥 : F.𝓥 ⟶ G.𝓥) :
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Over (P.HalfEdgeLabel × F.𝓔 × F.𝓥) ⥤ Over (P.HalfEdgeLabel × G.𝓔 × G.𝓥) :=
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Over.map <| edgeVertexMap 𝓔 𝓥
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@ -141,13 +141,11 @@ lemma normSq_eq_innerProd_self (φ : HiggsField) (x : SpaceTime) :
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-/
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@[simp]
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lemma normSq_apply_im_zero (φ : HiggsField) (x : SpaceTime) :
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((Complex.ofRealHom ‖φ x‖) ^ 2).im = 0 := by
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rw [sq]
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simp only [ofRealHom_eq_coe, mul_im, ofReal_re, ofReal_im, mul_zero, zero_mul, add_zero]
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@[simp]
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lemma normSq_apply_re_self (φ : HiggsField) (x : SpaceTime) :
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((Complex.ofRealHom ‖φ x‖) ^ 2).re = φ.normSq x := by
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rw [sq]
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@ -53,7 +53,7 @@ lemma coMetric_basis_expand : {η' | μ ν}ᵀ.tensor =
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rfl
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/-- Provides the explicit expansion of the co-metric tensor in terms of the basis elements, as
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a tensor tree.-/
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a tensor tree. -/
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lemma coMetric_basis_expand_tree : {η' | μ ν}ᵀ.tensor =
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(TensorTree.add (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 0))) <|
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TensorTree.add (smul (-1) (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 1)))) <|
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@ -33,7 +33,7 @@ import HepLean.Tensors.ComplexLorentz.Basic
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`{T | μ ν ⊗ T3 | μ σ}ᵀ` is `contr 0 1 _ (prodNode (tensorNode T1) (tensorNode T3))`.
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`{T | μ ν ⊗ T3 | μ ν }ᵀ` is
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`contr 0 0 _ (contr 0 1 _ (prodNode (tensorNode T1) (tensorNode T3)))`.
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- If `T4` is a tensor `S.F (OverColor.mk ![c2, c1])` then
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- If `T4` is a tensor `S.F (OverColor.mk ![c2, c1])` then
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`{T | μ ν + T4 | ν μ }ᵀ`is `addNode (tensorNode T) (perm _ (tensorNode T4))` where `_`
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is the permutation of the two indices of `T4`.
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`{T | μ ν = T4 | ν μ }ᵀ` is `(tensorNode T).tensor = (perm _ (tensorNode T4)).tensor` is the
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@ -42,8 +42,8 @@ import HepLean.Tensors.ComplexLorentz.Basic
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## Comments
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- In all of theses expressions `μ`, `ν` etc are free. It does not matter what they are called,
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Lean will elaborate them in the same way. I.e. `{T | μ ν ⊗ T3 | μ ν }ᵀ` is exactly the same
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to Lean as `{T | α β ⊗ T3 | α β }ᵀ`.
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Lean will elaborate them in the same way. I.e. `{T | μ ν ⊗ T3 | μ ν }ᵀ` is exactly the same
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to Lean as `{T | α β ⊗ T3 | α β }ᵀ`.
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- Note that compared to ordinary index notation, we do not rise or lower the indices.
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This is for two reasons: 1) It is difficult to make this general for all tensor species,
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2) It is a reduency in ordinary index notation, since the tensor `T` itself already tells you
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