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theorem proved term proof

scale_change_cost

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formal statement (Lean)

  45theorem scale_change_cost {c x : ℝ} (hc : 0 < c) (hx : 0 < x) :
  46    Jcost (c * x) ≤ 2 * Jcost c * Jcost x + 2 * Jcost c + 2 * Jcost x := by

proof body

Term-mode proof.

  47  have h := rcl_equality hc hx
  48  -- J(cx) + J(c/x) = 2J(c)J(x) + 2J(c) + 2J(x)
  49  -- J(cx) ≤ 2J(c)J(x) + 2J(c) + 2J(x) since J(c/x) ≥ 0
  50  linarith [Jcost_nonneg (div_pos hc hx)]
  51
  52/-- If c = 1 (no scale change), cost is zero. -/

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