Pure prod P basis Vector
TensorSpecies.Tensor.Pure.prodP_basisVector
Project documentation
Given two pure tensors p1 : Pure S c and p2 : Pure S c, prodP p p2 is the tensor product of those tensors returning an element in Pure S (Sum.elim c c1 ∘ ⇑finSumFinEquiv.symm). -/ def Pure.prodP {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} (p1 : Pure S c) (p2 : Pure S c1) : Pure S (Fin.append c c1) := Fin.addCases (fun i => LinearEquiv.cast (R := k)...
Exact Lean statement
lemma Pure.prodP_basisVector {n n1 : ℕ} {c : Fin n → C} {c1 : Fin n1 → C}
(φ : ComponentIdx c) (φ1 : ComponentIdx (S := S) c1) :
Pure.prodP (Pure.basisVector c φ) (Pure.basisVector c1 φ1) =
Pure.basisVector _ (ComponentIdx.prod.symm (φ, φ1))Formal artifact
Lean source
lemma Pure.prodP_basisVector {n n1 : ℕ} {c : Fin n → C} {c1 : Fin n1 → C} (φ : ComponentIdx c) (φ1 : ComponentIdx (S := S) c1) : Pure.prodP (Pure.basisVector c φ) (Pure.basisVector c1 φ1) = Pure.basisVector _ (ComponentIdx.prod.symm (φ, φ1)) := by ext i revert i rw [Fin.forall_fin_add] simp only [prodP_apply_castAdd, prodP_apply_natAdd] constructor · intro i symm simp only [basisVector, ComponentIdx.prod, Equiv.coe_fn_symm_mk, Fin.addCases_left, LinearEquiv.cast_apply] rw [basis_congr (c1 := (c i)) (by simp)] simp · intro i symm simp only [basisVector, ComponentIdx.prod, Equiv.coe_fn_symm_mk, Fin.addCases_right, LinearEquiv.cast_apply] rw [basis_congr (c1 := (c1 i)) (by simp)] simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Product.lean:155-175
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