Prod T equivariant
TensorSpecies.Tensor.prodT_equivariant
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
@[simp]
lemma prodT_equivariant {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C}
(g : G) (t : S.Tensor c) (t1 : S.Tensor c1) :
prodT (g • t) (g • t1) = g • prodT t t1Formal artifact
Lean source
@[simp]lemma prodT_equivariant {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} (g : G) (t : S.Tensor c) (t1 : S.Tensor c1) : prodT (g • t) (g • t1) = g • prodT t t1 := 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 · simp [prodT_pure, actionT_pure] · simp [actionT_smul, map_smul, ht] · simp [map_add, ht1, ht2] · simp [actionT_smul, map_smul, ht] · simp [map_add, ht1, ht2]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Product.lean:579-589
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