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formal statement (Lean)
116structure UniqueCostAxioms (F : ℝ → ℝ) : Prop where
117 symmetric : ∀ {x}, 0 < x → F x = F x⁻¹
118 unit : F 1 = 0
119 convex : StrictConvexOn ℝ (Set.Ioi 0) F
120 calibrated : deriv (deriv (F ∘ exp)) 0 = 1
121 continuousOn_pos : ContinuousOn F (Ioi 0)
122 coshAdd : FunctionalEquation.CoshAddIdentity F
123 dAlembert_smooth : FunctionalEquation.dAlembert_continuous_implies_smooth_hypothesis (FunctionalEquation.H F)
124 dAlembert_toODE : FunctionalEquation.dAlembert_to_ODE_hypothesis (FunctionalEquation.H F)
125 ode_cont : FunctionalEquation.ode_regularity_continuous_hypothesis (FunctionalEquation.H F)
126 ode_diff : FunctionalEquation.ode_regularity_differentiable_hypothesis (FunctionalEquation.H F)
127 ode_bootstrap : FunctionalEquation.ode_linear_regularity_bootstrap_hypothesis (FunctionalEquation.H F)
128
129/-- Jcost is continuous on ℝ₊ -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (15)
Lean names referenced from this declaration's body.
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H
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
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CoshAddIdentity
in IndisputableMonolith.Cost.FunctionalEquation
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dAlembert_continuous_implies_smooth_hypothesis
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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dAlembert_to_ODE_hypothesis
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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H
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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ode_linear_regularity_bootstrap_hypothesis
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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ode_regularity_continuous_hypothesis
in IndisputableMonolith.Cost.FunctionalEquation
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ode_regularity_differentiable_hypothesis
in IndisputableMonolith.Cost.FunctionalEquation
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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F
in IndisputableMonolith.Physics.AnchorPolicy
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F
in IndisputableMonolith.Physics.LeptonGenerations.TauStepDerivation
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F
in IndisputableMonolith.Pipelines
decl_use