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lemma proved tactic proof

abs_sub_le_width_of_memI

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formal statement (Lean)

  21lemma abs_sub_le_width_of_memI {I : Interval} {x y : ℝ}
  22  (hx : memI I x) (hy : memI I y) : |x - y| ≤ width I := by

proof body

Tactic-mode proof.

  23  have : I.lo ≤ x ∧ x ≤ I.hi := hx
  24  have : I.lo ≤ y ∧ y ≤ I.hi := hy
  25  have : x - y ≤ I.hi - I.lo := by linarith
  26  have : y - x ≤ I.hi - I.lo := by linarith
  27  have : -(I.hi - I.lo) ≤ x - y ∧ x - y ≤ I.hi - I.lo := by
  28    constructor
  29    · linarith
  30    · linarith
  31  simpa [width, abs_le] using this
  32
  33/-! ## Certificate schema -/
  34
  35/-- Anchor certificate: per-species residue intervals plus charge-wise gap intervals. -/

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