Prove2Me

Stop-loss risk comparison and limitations of floored risk principles: crPositivePart_nonnegative

Proved
ActuarialValuation.crPositivePart_nonnegative

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

actuarial-sciencecoherent-risk-measure-stop-lossformal-verification

An excess-loss amount cannot be negative.

Mathematical relation:

crPositivePart_nonnegativecrPositivePart\_nonnegative

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

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_crPositivePart
Formal statement
namespace ActuarialValuation

theorem crPositivePart_nonnegative (x : ℝ) : 0≤crPositivePart x := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics inspired by Promislow (2015), chapters 22, published book reference https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/; supporting published actuarial reference https://doi.org/10.1111/1467-9965.00068. The proposed model is rooted in Promislow chapter 22. The target Lean identity is an original derivation, not a verbatim published result. Published source page 412 gives the actuarial risk assessment chapter context; the Lean statement is an original derived target.
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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