Pure prod P component
TensorSpecies.Tensor.Pure.prodP_component
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_component {n m : ℕ} {c : Fin n → C} {c1 : Fin m → C}
(p : Pure S c) (p1 : Pure S c1)
(φ : ComponentIdx (Fin.append c c1)) :
(p.prodP p1).component φ = p.component (ComponentIdx.prod φ).1 *
p1.component (ComponentIdx.prod φ).2Formal artifact
Lean source
lemma Pure.prodP_component {n m : ℕ} {c : Fin n → C} {c1 : Fin m → C} (p : Pure S c) (p1 : Pure S c1) (φ : ComponentIdx (Fin.append c c1)) : (p.prodP p1).component φ = p.component (ComponentIdx.prod φ).1 * p1.component (ComponentIdx.prod φ).2 := by simp [component] rw [← finSumFinEquiv.prod_comp] simp only [finSumFinEquiv_apply_left, finSumFinEquiv_apply_right, Fintype.prod_sum_type] congr · funext x simp only [prodP_apply_castAdd, LinearEquiv.cast_apply, ComponentIdx.prod, Equiv.coe_fn_mk] generalize_proofs h1 h2 h3 generalize p x = p' generalize c x = c' at * subst h3 rfl · funext x simp only [prodP_apply_natAdd, LinearEquiv.cast_apply, ComponentIdx.prod, Equiv.coe_fn_mk] generalize_proofs h1 h2 h3 generalize p1 x = p1' generalize c1 x = c1' at * subst h3 rfl- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Product.lean:182-205
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