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theorem proved term proof

interactionDefect_eq_zero_of_separatelyAdditive

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formal statement (Lean)

  70theorem interactionDefect_eq_zero_of_separatelyAdditive
  71    {P : ℝ → ℝ → ℝ} (h : SeparatelyAdditive P) :
  72    ∀ u v : ℝ, interactionDefect P u v = 0 := by

proof body

Term-mode proof.

  73  rcases h with ⟨p, q, hP⟩
  74  intro u v
  75  unfold interactionDefect
  76  rw [hP u v, hP u 0, hP 0 v, hP 0 0]
  77  ring
  78
  79/-- Conversely: a combiner whose interaction defect is identically zero is
  80separately additive. The witness functions are `p(u) := P(u, 0) - P(0, 0)`
  81and `q(v) := P(0, v)`. -/

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