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import Mathlib.Analysis.InnerProductSpace.PiL2
open RCLike Real Filter
open Topology ComplexConjugate
open LinearMap (BilinForm)
open TensorProduct
open InnerProductSpace
open Inner
example
{E : Type*} [NormedAddCommGroup E] [InnerProductSpace E]
{F : Type*} [NormedAddCommGroup F] [InnerProductSpace F]
: 1 = 0 := by
let e : E →ₗ[] E →ₗ[] := innerₗ E
let f : F →ₗ[] F →ₗ[] := innerₗ F
let e₂ := TensorProduct.map₂ e f
let l := TensorProduct.lid
have : ∀ e1 e2 : E, ∀ f1 f2 : F, e₂ (e1 ⊗ f1) (e2 ⊗ f2) =
let X : InnerProductSpace.Core (E ⊗[] F) := {
inner := by
intro a b
exact TensorProduct.lid ((TensorProduct.map₂ (innerₗ E) (innerₗ F)) a b)
conj_symm := by
simp
intro x y
unfold innerₗ
simp
sorry
nonneg_re := _
definite := _
add_left := _
smul_left := _
}
let inner : E ⊗[𝕜] E → E ⊗[𝕜] E → 𝕜 :=
--let x := TensorProduct.lift
--E.inner
--TensorProduct.map₂
sorry
sorry