Prove2Me

Independent joint-life outcomes and probabilities: jlBothDead_symmetric

Proved
ActuarialValuation.jlBothDead_symmetric

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

actuarial-scienceformal-verificationjoint-life-mortality-profit

Both-dead probability is symmetric. 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_jlBothDead
Formal statement
namespace ActuarialValuation

theorem jlBothDead_symmetric (px py : ℝ) : jlBothDead px py=jlBothDead 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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