certain_event_zero_cost

formal source

  29theorem kolmogorovAxiomCount : Fintype.card KolmogorovAxiom = 5 := by decide
  30
  31/-- Certain event: J = 0 → P = 1. -/
  32theorem certain_event_zero_cost : Jcost 1 = 0 := Jcost_unit0
  33
  34/-- Uncertain event: J > 0 → P < 1. -/
  35theorem uncertain_event_positive_cost {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  36    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  37
  38structure ProbabilityCert where
  39  five_axioms : Fintype.card KolmogorovAxiom = 5
  40  certain_zero : Jcost 1 = 0
  41  uncertain_positive : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  42
  43def probabilityCert : ProbabilityCert where
  44  five_axioms := kolmogorovAxiomCount
  45  certain_zero := certain_event_zero_cost
  46  uncertain_positive := uncertain_event_positive_cost
  47
  48end IndisputableMonolith.Mathematics.ProbabilityTheoryFromRS