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theorem proved term proof

isCouplingCombiner_iff_interactionDefect_nonzero

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formal statement (Lean)

 100theorem isCouplingCombiner_iff_interactionDefect_nonzero
 101    (P : ℝ → ℝ → ℝ) :
 102    IsCouplingCombiner P ↔ ∃ u v : ℝ, interactionDefect P u v ≠ 0 := by

proof body

Term-mode proof.

 103  unfold IsCouplingCombiner
 104  rw [separatelyAdditive_iff_interactionDefect_zero]
 105  constructor
 106  · intro h
 107    by_contra hno
 108    push_neg at hno
 109    exact h hno
 110  · rintro ⟨u, v, huv⟩ hall
 111    exact huv (hall u v)
 112
 113/-! ## The RCL Combiner -/
 114
 115/-- The polynomial combiner attached to the RCL family with parameter
 116`c`: `P(u, v) = 2u + 2v + c·u·v`. -/

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