Pure prod P perm P left
TensorSpecies.Tensor.Pure.prodP_permP_left
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
@[simp]
lemma Pure.prodP_permP_left {n n'} {c : Fin n → C} {c' : Fin n' → C}
(σ : Fin n' → Fin n) (h : IsReindexing c c' σ) (p : Pure S c) (p2 : Pure S c2) :
Pure.prodP (permP σ h p) p2 = permP _ (h.append_congr_left c2) (Pure.prodP p p2)Formal artifact
Lean source
@[simp]lemma Pure.prodP_permP_left {n n'} {c : Fin n → C} {c' : Fin n' → C} (σ : Fin n' → Fin n) (h : IsReindexing c c' σ) (p : Pure S c) (p2 : Pure S c2) : Pure.prodP (permP σ h p) p2 = permP _ (h.append_congr_left c2) (Pure.prodP p p2) := by ext i refine Fin.addCases (fun i => ?_) (fun i => ?_) i · have h0 : (i.castAdd n2).append (Fin.castAdd n2 ∘ σ) (Fin.natAdd n) = (σ i).castAdd n2 := by simp simp [permP, ← congr_right _ _ _ h0] · have h0 : (i.natAdd n').append (Fin.castAdd n2 ∘ σ) (Fin.natAdd n) = i.natAdd n := by simp simp [permP, ← congr_right _ _ _ h0]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Product.lean:273-283
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