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refactor: lint

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jstoobysmith 2024-11-18 14:13:44 +00:00
parent ce0805bbdd
commit dcf6b774d4
12 changed files with 126 additions and 61 deletions
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6
HepLean/Tensors/TensorSpecies/UnitTensor.lean
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@ -113,7 +113,7 @@ lemma dual_unitTensor_eq_perm (c : S.C) :
rfl
/-- Applying `contrOneTwoLeft` with the unit tensor is the identity map. -/
lemma contrOneTwoLeft_unitTensor {c1 : S.C} (x : S.F.obj (OverColor.mk ![c1])) :
lemma contrOneTwoLeft_unitTensor {c1 : S.C} (x : S.F.obj (OverColor.mk ![c1])) :
contrOneTwoLeft x (S.unitTensor c1) = x := by
simp only [Nat.succ_eq_add_one, Nat.reduceAdd, contrOneTwoLeft,
Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
@ -131,14 +131,14 @@ lemma contrOneTwoLeft_unitTensor {c1 : S.C} (x : S.F.obj (OverColor.mk ![c1]))
/-- Contracting a vector with a unit tensor returns the vector. -/
lemma vec_contr_unitTensor_eq_self {c1 : S.C} (x : S.F.obj (OverColor.mk ![c1])) :
{x | μ ⊗ S.unitTensor c1 | μ ν}ᵀ.tensor = ({x | ν}ᵀ |>
perm (OverColor.equivToHomEq (Equiv.refl _) (fun x => by fin_cases x; rfl ))).tensor := by
perm (OverColor.equivToHomEq (Equiv.refl _) (fun x => by fin_cases x; rfl))).tensor := by
rw [contr_one_two_left_eq_contrOneTwoLeft, contrOneTwoLeft_unitTensor]
rfl
/-- Contracting a unit tensor with a vector returns the unit vector. -/
lemma unitTensor_contr_vec_eq_self {c1 : S.C} (x : S.F.obj (OverColor.mk ![S.τ c1])) :
{S.unitTensor c1 | ν μ ⊗ x | μ}ᵀ.tensor = ({x | ν}ᵀ |>
perm (OverColor.equivToHomEq (Equiv.refl _) (fun x => by fin_cases x; rfl ))).tensor := by
perm (OverColor.equivToHomEq (Equiv.refl _) (fun x => by fin_cases x; rfl))).tensor := by
conv_lhs =>
rw [contr_tensor_eq <| prod_comm _ _ _ _]
rw [perm_contr_congr 2 0 (by simp; decide) (by simp; decide)]