Prove2Me

Finite commutation functions: commSurvivorSum_zero

Proved
ActuarialValuation.commSurvivorSum_zero

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

actuarial-scienceformal-verificationlife-commutation-functions

Zero duration contains no annuity payment dates. The full Lean declaration specifies the finite boundaries, exact units and any positivity, independence or regularity assumptions. This is an original derived Actuarial mathematical statement, not a claim of a numbered previously published theorem.

Mathematical relation:

Nx:0=0N_{x:0}=0
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_commSurvivorSum
Formal statement
namespace ActuarialValuation

theorem commSurvivorSum_zero (l : ℕ → ℝ) (v : ℝ) (x : ℕ) : commSurvivorSum l v x 0 = 0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 50. Institute of Actuaries, International Actuarial Notation, Commutation Functions, https://www.actuaries.org.uk/system/files/documents/pdf/0042-0071.pdf; Dickson, Hardy and Waters, Actuarial Mathematics for Life Contingent Risks (2009), Chapter 5, Annuities, https://www.cambridge.org/core/books/abs/actuarial-mathematics-for-life-contingent-risks/annuities/6E4AF10872F5D04E3437447F025ECA97. Parent topic: Discounted survivor and death functions, term annuities, term assurances, endowment and finite-life present value decomposition. The particular Lean formula is a new finite/real-algebraic formalisation and remains an unproved theorem target if labelled theorem. Relevant published actuarial derivation: https://www.actuaries.org.uk/system/files/documents/pdf/0042-0071.pdf
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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