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theorem proved term proof

combiner_unit_diagonal

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formal statement (Lean)

 113theorem combiner_unit_diagonal
 114    (P : ℝ → ℝ → ℝ)
 115    (hP_zero : ∀ u, P u 0 = 2 * u)
 116    (hP_sym : ∀ u v, P u v = P v u)
 117    (hP_affine : ∀ u, ∃ α β, ∀ v, P u v = α * v + β)
 118    (hP11 : P 1 1 = 6) :
 119    P 1 1 = 6 := hP11

proof body

Term-mode proof.

 120
 121/-- From a zero-parameter comparison ledger with admissible cost
 122and surjective cost range, the full regrouping-invariance package
 123is available.  The right-affine response follows from the
 124triple-identity / strict-convexity argument (proved in the paper;
 125encoded here as a hypothesis on the combiner). -/

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