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def definition def or abbrev

embedState

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formal statement (Lean)

 529def embedState {d N : ℕ} (_h : d ≤ Fintype.card (CoupledCoreIndex N)) :
 530    (Fin d → ℂ) →ₗ[ℂ] CoupledCoreSpace N where
 531  toFun := fun v s =>

proof body

Definition body.

 532    let i := coupledCoreEquivFin N s
 533    if hi : i.val < d then v ⟨i.val, hi⟩ else 0
 534  map_add' := by
 535    intro v w
 536    ext s
 537    dsimp [coupledCoreEquivFin]
 538    split_ifs <;> simp
 539  map_smul' := by
 540    intro z v
 541    ext s
 542    dsimp [coupledCoreEquivFin]
 543    split_ifs <;> simp
 544
 545/-- Restrict a coupled-core state back to the first `d` coordinates of the
 546enumerated basis. -/

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depends on (11)

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