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theorem proved tactic proof

edge_deviation_small

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formal statement (Lean)

  68theorem edge_deviation_small {r : ℝ} (hr : 0 < r) {δ : ℝ} (hδ : 0 ≤ δ)
  69    (hδ_small : δ ≤ 1) (hJ : Jcost r ≤ δ) : (r - 1) ^ 2 ≤ 8 * δ := by

proof body

Tactic-mode proof.

  70  have h := edge_deviation_bound hr hδ hJ
  71  calc (r - 1) ^ 2 ≤ 4 * δ * (1 + δ) := h
  72    _ ≤ 4 * δ * (1 + 1) := by nlinarith
  73    _ = 8 * δ := by ring
  74
  75/-- Absolute deviation bound: |r - 1| ≤ √(8δ) for δ ≤ 1. -/

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