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formal statement (Lean)
44structure ProbDist (ι : Type*) [Fintype ι] where
45 prob : ι → ℝ
46 prob_pos : ∀ i, 0 < prob i
47 prob_sum : ∑ i, prob i = 1
48
49theorem ProbDist.prob_nonneg (q : ProbDist ι) (i : ι) : 0 ≤ q.prob i :=
proof body
Definition body.
50 le_of_lt (q.prob_pos i)
51
52/-- The variational free energy F[q ; E, β]. -/
used by (24)
From the project-wide theorem graph. These declarations reference this one in their body.
-
deterministic_has_zero_entropy
in IndisputableMonolith.Information.InformationIsLedger
decl_use
-
entropy_nonneg
in IndisputableMonolith.Information.InformationIsLedger
decl_use
-
shannon_entropy_equals_expected_jcost
in IndisputableMonolith.Information.InformationIsLedger
decl_use
-
entropy_is_expected_surprisal
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
entropy_nonneg
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
ProbDist
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
shannonEntropy
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
shannon_equals_jcost
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
totalJCost
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
uniform
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
zero_entropy_deterministic
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
BayesianFilteringCert
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
bayesStep
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
bayesStep_is_update
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
evidence
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
evidence_pos
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
iterFilter
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
iterFilter_cons
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
iterFilter_nil
in IndisputableMonolith.Statistics.BayesianFilteringFromVFE
decl_use
-
boltzmannDist
in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL
decl_use
-
boltzmann_minimizes_vfe
in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL
decl_use
-
kl_nonneg
in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL
decl_use
-
VFE
in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL
decl_use
-
VFECert
in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL
decl_use
depends on (12)
Lean names referenced from this declaration's body.
-
prob
in IndisputableMonolith.Decision.StPetersburg
decl_use
-
prob
in IndisputableMonolith.Decision.StPetersburg
decl_use
-
prob_pos
in IndisputableMonolith.Decision.StPetersburg
decl_use
-
prob_pos
in IndisputableMonolith.Decision.StPetersburg
decl_use
-
prob_nonneg
in IndisputableMonolith.Foundation.QuantumLedger
decl_use
-
E
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
-
ProbDist
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
ProbDist
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
F
in IndisputableMonolith.Physics.AnchorPolicy
decl_use
-
F
in IndisputableMonolith.Physics.LeptonGenerations.TauStepDerivation
decl_use
-
F
in IndisputableMonolith.Pipelines
decl_use
-
prob_nonneg
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use