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Foundation /
Foundation.GeneralizedDAlembert /
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formal statement (Lean)
544 def ContinuousCombinerSecondDerivativeInput
545 (C : ComparisonOperator)
546 (_h : SatisfiesLawsOfLogicContinuous C)
547 (_hSmooth : ContDiff ℝ ((⊤ : ℕ∞) : WithTop ℕ∞)
548 (fun t : ℝ => derivedCost C (Real.exp t))) : Prop :=
proof body
Definition body.
549 AczelSecondDerivativeIdentity (fun t : ℝ => derivedCost C (Real.exp t))
550
551 /-- **Named analysis input 2b: ψ-affine completion.**
552
553 This is the remaining Stetkær/Aczél content: the derivative identity, symmetry
554 of the combiner, and the Aczél equation force the actual log-bilinear identity.
555 It is narrower than the former all-in ψ-affine forcing axiom because the
556 second-derivative extraction is now named separately. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (20)
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AczelSecondDerivativeIdentity
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SatisfiesLawsOfLogicContinuous
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ComparisonOperator
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derivedCost
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