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theorem proved tactic proof

AApply_sq

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formal statement (Lean)

 119theorem AApply_sq {n : ℕ}
 120    (lam : ℝ) (hInv : Fin n → Fin n → ℝ) (β v : Vec n) :
 121    AApply lam hInv β (AApply lam hInv β v) = mu lam hInv β • AApply lam hInv β v := by

proof body

Tactic-mode proof.

 122  funext i
 123  have hdot :
 124      dot β (fun k => lam * sharp hInv β k * dot β v) = mu lam hInv β * dot β v := by
 125    simpa [AApply] using dot_AApply lam hInv β v
 126  unfold AApply
 127  rw [hdot]
 128  simp [mu]
 129  ring
 130

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