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theorem proved term proof

gm_pair_unity

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formal statement (Lean)

 100theorem gm_pair_unity {x : ℝ} (hx : 0 < x) : Real.sqrt (x * x⁻¹) = 1 := by

proof body

Term-mode proof.

 101  rw [mul_inv_cancel₀ (ne_of_gt hx), Real.sqrt_one]
 102
 103/-- Jcost x = AM(x, x⁻¹) − GM(x, x⁻¹).
 104    The recognition cost is the AM-GM gap of the pair {x, x⁻¹}. -/

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