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refactor: Some basic golfings

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jstoobysmith 2024-12-20 10:47:34 +00:00
parent c739a5eeb8
commit 6db7f86471
5 changed files with 44 additions and 70 deletions
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22
HepLean/Lorentz/ComplexTensor/PauliMatrices/Basis.lean
View file

@ -342,28 +342,28 @@ lemma pauliMatrix_contr_down_0 :
lhs
rw [basis_contr_pauliMatrix_basis_tree_expand_tensor]
conv =>
lhs; lhs; lhs; lhs; lhs; lhs; lhs; lhs
enter [1, 1, 1, 1, 1, 1, 1, 1]
rw [contrBasisVectorMul_pos (by decide)]
conv =>
lhs; lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
enter [1, 1, 1, 1, 1, 1, 1, 2, 1]
rw [contrBasisVectorMul_pos (by decide)]
conv =>
lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
enter [1, 1, 1, 1, 1, 1, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; lhs; lhs; lhs; rhs; lhs
enter [1, 1, 1, 1, 1, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; lhs; lhs; rhs; rhs; lhs
enter [1, 1, 1, 1, 2, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; lhs; rhs; rhs; lhs
enter [1, 1, 1, 2, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; rhs; lhs;
enter [1, 1, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; rhs; rhs; lhs;
enter [1, 2, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs
@ -416,12 +416,10 @@ lemma pauliMatrix_contr_down_1 :
congr 1
· rw [basisVectorContrPauli]
congr 1
funext k
fin_cases k <;> rfl
decide
· rw [basisVectorContrPauli]
congr 1
funext k
fin_cases k <;> rfl
decide
lemma pauliMatrix_contr_down_2 :
{(basisVector ![Color.down, Color.down] fun _ => 2) | μ ν ⊗

65
HepLean/Lorentz/ComplexTensor/PauliMatrices/CoContractContr.lean
View file

@ -92,28 +92,28 @@ lemma pauliMatrix_contr_lower_0_1_1 :
lhs
rw [basis_contr_pauliMatrix_basis_tree_expand_tensor]
conv =>
lhs; lhs; lhs; lhs; lhs; lhs; lhs; lhs
enter [1, 1, 1, 1, 1, 1, 1, 1]
rw [contrBasisVectorMul_pos (by decide)]
conv =>
lhs; lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
enter [1, 1, 1, 1, 1, 1, 1, 2, 1]
rw [contrBasisVectorMul_pos (by decide)]
conv =>
lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
enter [1, 1, 1, 1, 1, 1, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; lhs; lhs; lhs; rhs; lhs
enter [1, 1, 1, 1, 1, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; lhs; lhs; rhs; rhs; lhs
enter [1, 1, 1, 1, 2, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; lhs; rhs; rhs; lhs
enter [1, 1, 1, 2, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; lhs; rhs; lhs;
enter [1, 1, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs; rhs; rhs; lhs;
enter [1, 2, 2, 1]
rw [contrBasisVectorMul_neg (by decide)]
conv =>
lhs
@ -122,11 +122,9 @@ lemma pauliMatrix_contr_lower_0_1_1 :
/- Simplifying. -/
congr 1
· congr 1
funext k
fin_cases k <;> rfl
decide
· congr 1
funext k
fin_cases k <;> rfl
decide
lemma pauliMatrix_contr_lower_1_0_1 :
{(basisVector pauliCoMap (fun | 0 => 1 | 1 => 0 | 2 => 1)) | μ α β ⊗
@ -212,12 +210,9 @@ lemma pauliMatrix_contr_lower_1_1_0 :
/- Simplifying. -/
congr 1
· congr 1
funext k
fin_cases k <;> rfl
decide
· congr 1
funext k
fin_cases k <;> rfl
decide
lemma pauliMatrix_contr_lower_2_0_1 :
{(basisVector pauliCoMap (fun | 0 => 2 | 1 => 0 | 2 => 1)) | μ α β ⊗
pauliContr | μ α' β'}ᵀ.tensor =
@ -258,11 +253,9 @@ lemma pauliMatrix_contr_lower_2_0_1 :
/- Simplifying. -/
congr 1
· congr 2
funext k
fin_cases k <;> rfl
decide
· congr 2
funext k
fin_cases k <;> rfl
decide
lemma pauliMatrix_contr_lower_2_1_0 :
{(basisVector pauliCoMap (fun | 0 => 2 | 1 => 1 | 2 => 0)) | μ α β ⊗
@ -304,11 +297,9 @@ lemma pauliMatrix_contr_lower_2_1_0 :
/- Simplifying. -/
congr 1
· congr 2
funext k
fin_cases k <;> rfl
decide
· congr 2
funext k
fin_cases k <;> rfl
decide
lemma pauliMatrix_contr_lower_3_0_0 :
{(basisVector pauliCoMap (fun | 0 => 3 | 1 => 0 | 2 => 0)) | μ α β ⊗
@ -350,11 +341,9 @@ lemma pauliMatrix_contr_lower_3_0_0 :
/- Simplifying. -/
congr 1
· congr 2
funext k
fin_cases k <;> rfl
decide
· congr 2
funext k
fin_cases k <;> rfl
decide
lemma pauliMatrix_contr_lower_3_1_1 :
{(basisVector pauliCoMap (fun | 0 => 3 | 1 => 1 | 2 => 1)) | μ α β ⊗
@ -396,11 +385,9 @@ lemma pauliMatrix_contr_lower_3_1_1 :
/- Simplifying. -/
congr 1
· congr 2
funext k
fin_cases k <;> rfl
decide
· congr 2
funext k
fin_cases k <;> rfl
decide
/-! TODO: Work out why `pauliCo_prod_basis_expand'` is needed. -/
/-- This lemma is exactly the same as `pauliCo_prod_basis_expand`.
@ -549,13 +536,9 @@ theorem pauliCo_contr_pauliContr :
abel
rw [h1]
congr
· funext i
fin_cases i <;> rfl
· funext i
fin_cases i <;> rfl
· funext i
fin_cases i <;> rfl
· funext i
fin_cases i <;> rfl
· decide
· decide
· decide
· decide
end complexLorentzTensor