Prod T assoc
TensorSpecies.Tensor.prodT_assoc
Project documentation
Rewriting basis for the product in terms of the tensor product basis. -/ lemma basis_prod_eq {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} : basis (S := S) (Fin.append c c1) = (((Tensor.basis (S := S) c).tensorProduct (Tensor.basis (S := S) c1)).reindex (ComponentIdx.prod.symm)).map tensorEquivProd := by ext b simp [ComponentIdx.prod, tensorEquivProd] rw [pr...
Exact Lean statement
lemma prodT_assoc {n n1 n2} {c : Fin n → C}
{c1 : Fin n1 → C} {c2 : Fin n2 → C} (t : S.Tensor c) (t1 : S.Tensor c1) (t2 : S.Tensor c2) :
prodT (prodT t t1) t2 = permT _ IsReindexing.append_assoc_right (prodT t (prodT t1 t2))Formal artifact
Lean source
lemma prodT_assoc {n n1 n2} {c : Fin n → C} {c1 : Fin n1 → C} {c2 : Fin n2 → C} (t : S.Tensor c) (t1 : S.Tensor c1) (t2 : S.Tensor c2) : prodT (prodT t t1) t2 = permT _ IsReindexing.append_assoc_right (prodT t (prodT t1 t2)) := by induction' t using induction_on_pure with p r t ht t1 t2 ht1 ht2 · induction' t1 using induction_on_pure with q r t ht t1 t2 ht1 ht2 · induction' t2 using induction_on_pure with q r t ht t1 t2 ht1 ht2 · simp [prodT_pure, permT_pure, Pure.prodP_assoc] · simp [ht] · simp [ht1, ht2] · simp [ht] · simp [ht1, ht2] · simp [ht] · simp [ht1, ht2]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Product.lean:677-689
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