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lemma proved term proof

modal_distance_nonneg

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formal statement (Lean)

  55lemma modal_distance_nonneg (c1 c2 : Config) : 0 ≤ modal_distance c1 c2 := by

proof body

Term-mode proof.

  56  unfold modal_distance J_transition
  57  apply mul_nonneg (abs_nonneg _)
  58  apply div_nonneg
  59  · apply add_nonneg (J_nonneg c1.pos) (J_nonneg c2.pos)
  60  · norm_num
  61
  62/-- Modal distance to self is zero. -/

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