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fix: Correct tensor evaluation

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jstoobysmith 2024-10-21 14:28:02 +00:00
parent 7fc850cc38
commit baf5169171
2 changed files with 18 additions and 2 deletions
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19
HepLean/Tensors/ComplexLorentz/Lemmas.lean
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@ -89,7 +89,8 @@ lemma contr_rank_2_symm {T1 : (Lorentz.complexContr ⊗ Lorentz.complexContr).V}
rw [perm_perm]
rw [perm_eq_id]
· rfl
· rfl
· apply OverColor.Hom.ext
rfl
· apply OverColor.Hom.ext
ext x
exact Fin.elim0 x
@ -104,6 +105,7 @@ lemma contr_rank_2_symm' {T1 : (Lorentz.complexCo ⊗ Lorentz.complexCo).V}
ext x
exact Fin.elim0 x
set_option maxRecDepth 20000 in
/-- Contracting a rank-2 anti-symmetric tensor with a rank-2 symmetric tensor gives zero. -/
lemma antiSymm_contr_symm {A : (Lorentz.complexContr ⊗ Lorentz.complexContr).V}
{S : (Lorentz.complexCo ⊗ Lorentz.complexCo).V}
@ -120,7 +122,20 @@ lemma antiSymm_contr_symm {A : (Lorentz.complexContr ⊗ Lorentz.complexContr).V
rw [contr_tensor_eq (contr_tensor_eq (neg_fst_prod _ _))]
rw [contr_tensor_eq (neg_contr _)]
rw [neg_contr]
rfl
rw [neg_tensor]
apply congrArg
rw [contr_tensor_eq (contr_tensor_eq (prod_perm_left _ _ _ _))]
rw [contr_tensor_eq (perm_contr _ _)]
rw [perm_contr]
rw [perm_tensor_eq (contr_tensor_eq (contr_tensor_eq (prod_perm_right _ _ _ _)))]
rw [perm_tensor_eq (contr_tensor_eq (perm_contr _ _))]
rw [perm_tensor_eq (perm_contr _ _)]
rw [perm_perm]
nth_rewrite 1 [perm_tensor_eq (contr_contr _ _ _)]
rw [perm_perm]
rw [perm_eq_id]
· rfl
· rfl
lemma symm_contr_antiSymm {S : (Lorentz.complexCo ⊗ Lorentz.complexCo).V}
{A : (Lorentz.complexContr ⊗ Lorentz.complexContr).V}