Pure prod P equivariant
TensorSpecies.Tensor.Pure.prodP_equivariant
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_equivariant {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C}
(g : G) (p : Pure S c) (p1 : Pure S c1) :
prodP (g • p) (g • p1) = g • prodP p p1Formal artifact
Lean source
@[simp]lemma Pure.prodP_equivariant {n1 n2} {c : Fin n1 → C} {c1 : Fin n2 → C} (g : G) (p : Pure S c) (p1 : Pure S c1) : prodP (g • p) (g • p1) = g • prodP p p1 := by ext i revert i rw [Fin.forall_fin_add] simp only [actionP_eq, prodP_apply_castAdd, prodP_apply_natAdd] constructor · intro j generalize_proofs h1 h2 generalize p j = p' generalize c j = c' at * subst h2 rfl · intro j generalize_proofs h1 h2 generalize p1 j = p1' generalize c1 j = c1' at * subst h2 rfl- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Product.lean:213-233
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