Prove2Me

Frequency-dependent annuity cashflow valuation: frDueValue_empty

Proved
ActuarialValuation.frDueValue_empty

by WillR · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

actuarial-scienceformal-verificationfractional-life-valuation

A zero-year due annuity has no payment times and zero present value.

Mathematical relation:

frDueValue_emptyfrDueValue\_empty

Original derived theorem target; the Lean statement gives the exact conditions and result.

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Analysis.SpecialFunctions.Exp
import Definitions.Def_actuarial_frDueValue
Formal statement
namespace ActuarialValuation

theorem frDueValue_empty (c : ℕ → ℝ) (discount : ℝ → ℝ) (p q : ℕ → ℝ) (m : ℕ) : frDueValue c discount p q 0 m = 0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics inspired by Promislow (2015), chapters 7, 4 and 8, published book reference https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/; supporting published actuarial reference https://www.soa.org/498941/globalassets/assets/files/e-business/pd/events/2018/las/pd-2018-05-las-session-033.pdf. Published source page 98 of Promislow's 2015 edition provides the thematic mathematical context. The target Lean identity is an original derivation, not a verbatim published result.
Human review

  • Endorsed by Shuze Chen · Oct 11, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 11, 2026

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

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