`BookProof.TwoParticleSector.tensorSquare_induction` {Y : Type} [NormedAddCommGroup Y] [InnerProductSpace ℂ Y] {P : Y ⊗[ℂ] (Y ⊗[ℂ] ℂ) → Prop} (hzero : P 0) (htmul : ∀ (x y : Y) (c

Proved

BookProof.TwoParticleSector.tensorSquare_induction

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTwoParticleSectorEsa.

BookProof.TwoParticleSector.tensorSquare_induction {Y : Type} [NormedAddCommGroup Y] [InnerProductSpace ℂ Y] {P : Y ⊗[ℂ] (Y ⊗[ℂ] ℂ) → Prop} (hzero : P 0) (htmul : ∀ (x y : Y) (c : ℂ), P (x ⊗ₜ[ℂ] (y ⊗ₜ[ℂ] c))) (hadd : ∀ u v, P u → P v → P (u + v)) (t : Y ⊗[ℂ] (Y ⊗[ℂ] ℂ)) : P t

Formalization note: Lean 4 identifier BookProof.TwoParticleSector.tensorSquare_induction.

Preamble

-- Generated from ChapterTwoParticleSectorEsa.lean — theorem BookProof.TwoParticleSector.tensorSquare_induction
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterReducingSubspaceEsa
import Definitions.Def_ChapterTensorGraphCore
import Mathlib
import Definitions.Def_ChapterTwoParticleSectorEsa
open BookProof.TwoParticleSector



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore BookProof.ReducedEsa BookProof.TensorCore

noncomputable section

variable (X : Type) [NormedAddCommGroup X] [InnerProductSpace ℂ X]
variable {X}
variable (Hs : IPSpace) (D₂ : Submodule ℂ Hs.carrier)

Formal statement

theorem BookProof.TwoParticleSector.tensorSquare_induction {Y : Type} [NormedAddCommGroup Y] [InnerProductSpace ℂ Y]
    {P : Y ⊗[ℂ] (Y ⊗[ℂ] ℂ) → Prop} (hzero : P 0)
    (htmul : ∀ (x y : Y) (c : ℂ), P (x ⊗ₜ[ℂ] (y ⊗ₜ[ℂ] c)))
    (hadd : ∀ u v, P u → P v → P (u + v)) (t : Y ⊗[ℂ] (Y ⊗[ℂ] ℂ)) : P t := by sorry

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