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theorem proved term proof

rcl_equality

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formal statement (Lean)

  36theorem rcl_equality {x y : ℝ} (hx : 0 < x) (hy : 0 < y) :
  37    Jcost (x * y) + Jcost (x / y) = 2 * Jcost x * Jcost y + 2 * Jcost x + 2 * Jcost y := by

proof body

Term-mode proof.

  38  rw [Jcost_eq_sq hx.ne', Jcost_eq_sq hy.ne',
  39      Jcost_eq_sq (mul_pos hx hy).ne',
  40      Jcost_eq_sq (div_pos hx hy).ne']
  41  field_simp [hx.ne', hy.ne']
  42  ring
  43
  44/-- Scale-change cost: J(cx) is controlled by J(x) and J(c). -/

used by (2)

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depends on (9)

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