Prove2Me

Later survival probability cannot exceed earlier

Proved
actuarial_c_survival_monotone

by WillR · Oct 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

actuarial-scienceinsurancelife-contingency

Later survival probability cannot exceed earlier.

Mathematical relation:

S(j)≤S(i),i≤jS(j)\le S(i),\quad i\le j

For this statement, the yearly death event, valuation origin and life-law normalisation follow the stated hypotheses. Death benefits are settled at the end of the policy year, whereas a maturity amount is payable at its anniversary. Every formula represents a currently open formal obligation unless it is a definition.

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_c_alive
import Definitions.Def_actuarial_c_surv

open ActuarialAssurances
Formal statement
theorem actuarial_c_survival_monotone (h i j : ℕ) (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) (hij : i ≤ j) : surv h p j ≤ surv h p i := by sorry
Source
Original derived finite life-contingency specification; S. David Promislow (2015), Fundamentals of Actuarial Mathematics, 3rd edition, Chapter 5, Sections 5.1–5.2, occurrence and death-year timing, printed p. 61. https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml. The cited material establishes actuarial context and payment conventions. This particular finite Lean declaration is not a verbatim published theorem.
Human review

  • Endorsed by Shuze Chen · Oct 13, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 13, 2026

    Confirmed by the mission captain (proposal self-audit).

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