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theorem proved term proof

lattice_gap_witness

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formal statement (Lean)

  44theorem lattice_gap_witness (a : ℝ) (ha : 0 < a) : latticeSpacingGap a ha := by

proof body

Term-mode proof.

  45  unfold latticeSpacingGap
  46  refine ⟨Jcost (1 + a) / 2, ?_, ?_⟩
  47  · apply div_pos
  48    · exact Jcost_pos_of_ne_one _ (by linarith) (by linarith)
  49    · norm_num
  50  · linarith [Jcost_pos_of_ne_one (1 + a) (by linarith) (by linarith)]
  51

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