Prove2Me

Independent joint-life outcomes and probabilities: jlBothAlive_symmetric

Proved
ActuarialValuation.jlBothAlive_symmetric

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

actuarial-scienceformal-verificationjoint-life-mortality-profit

Joint survival is symmetric in two independent insured lives. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

pxy=pxpy,px†y=(1−px)pyp_{xy}=p_xp_y,\quad p_{x\dagger y}=(1-p_x)p_y
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Definitions.Def_actuarial_jlBothAlive
Formal statement
namespace ActuarialValuation

theorem jlBothAlive_symmetric (px py : ℝ) : jlBothAlive px py=jlBothAlive py px := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 132. Dickson, Hardy and Waters (2020), Actuarial Mathematics for Life Contingent Risks, multiple life insurance and reserves, https://www.cambridge.org/core/books/actuarial-mathematics-for-life-contingent-risks/; S. D. Promislow (2015), Fundamentals of Actuarial Mathematics, multiple-life theory. Parent topic: Independent joint-life outcome probabilities, distinct survivors' reserves, outcome-specific death strain and mortality profit reconciliation with guaranteed reversionary benefits. 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.cambridge.org/core/books/actuarial-mathematics-for-life-contingent-risks/
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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