lemma
proved
term proof
boltzmannFactor_pos
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formal statement (Lean)
80lemma boltzmannFactor_pos (level : EnergyLevel) (beta : ℝ) :
81 boltzmannFactor level beta > 0 := by
proof body
Term-mode proof.
82 unfold boltzmannFactor
83 apply mul_pos
84 · exact Nat.cast_pos.mpr level.deg_pos
85 · exact exp_pos _
86
87/-- Helper: sum of positive list is nonneg -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (16)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
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boltzmannFactor
in IndisputableMonolith.Chemistry.ActivationEnergy
decl_use
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boltzmannFactor
in IndisputableMonolith.Chemistry.EnzymeCatalysis
decl_use
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
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boltzmannFactor
in IndisputableMonolith.Information.ShannonEntropy
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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beta
in IndisputableMonolith.Relativity.ILG.PPN
decl_use
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boltzmannFactor
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
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EnergyLevel
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
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beta
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use