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formal statement (Lean)
216theorem deriv_Jcost_one : deriv Jcost 1 = 0 := by
proof body
Term-mode proof.
217 have h : HasDerivAt Jcost ((1 - 1⁻¹ ^ 2) / 2) 1 := hasDerivAt_Jcost 1 (by norm_num)
218 simp at h
219 exact h.deriv
220
221/-!
222## Strict Convexity of Jcost
223
224The theorem `Jcost_strictConvexOn_pos : StrictConvexOn ℝ (Set.Ioi 0) Jcost`
225is proven in `Cost/Convexity.lean` using the second derivative approach:
226J''(x) = x⁻³ > 0 for x > 0.
227
228Import `IndisputableMonolith.Cost.Convexity` to access this theorem.
229-/
230
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (13)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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hasDerivAt_Jcost
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Jcost_strictConvexOn_pos
in IndisputableMonolith.Cost.Convexity
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of
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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of
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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Cost
in IndisputableMonolith.Measurement.RSNative.Core
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