Official Lean's own kernel accepts the 73 constructed-real declarations it will not take as theorems, once they are exported as definitions

Identifier: F:lean-kernel-accepts-the-non-prop-residue-of-the-constructed-real-carrier
Proof route: Not assigned
External status: unknown
Axiom footprint: Empty

Recorded description

The 73 declarations of the constructed-real carrier that pinned Lean 4.30.0's kernel refuses -- 48 Theorems whose type is not a proposition, and 25 whose dependency closure reaches one -- are accepted by that same kernel when the Type-valued carriers are exported as definitions rather than theorems, so that the whole carrier, and not only its representable population, holds an independent-replay grade. OPEN: nothing in this ledger has established it, and the export change it needs is a change to what `theorem` means on the wire.

Formal statement

Let K be the kernel state after `build_creal_prelude(&mut Kernel::new())` and let N be the non-representable population of `F:lean-kernel-accepts-the-whole-constructed-real-carrier` -- the `Declaration::Theorem`s whose type is not a proposition, together with everything whose `declaration_dependency_closure` reaches one (73 of 2,058 on 2026-08-30; 48 + 25). Then there is an encoding E of K's complete checked environment, agreeing with `render_lean4export_ndjson` on every representable declaration and differing from it only in emitting each element of N under a declaration kind Lean's kernel admits (a `def`, whose value is the same proof term), such that folding `Lean.Environment.addDeclCore` over E from `mkEmptyEnvironment` under the pinned Lean 4.30.0 (commit d024af099ca4bf2c86f649261ebf59565dc8c622) succeeds, and the resulting environment holds exactly `K.environment().iter().count()` constants -- including `CReal.weierstrassMTest`, `CReal.rolle_interiorExtremum` and `CReal.mvt_interiorExtremum` by name.

Dependencies

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1 direct dependencies 0 direct dependents

Evidence

Provenance

{
  "date": "2026-08-30",
  "established_by": "not established in this ledger",
  "source": "Split out of `F:lean-kernel-accepts-the-whole-constructed-real-carrier` when that fact's whole-carrier claim was corrected to its representable population (ADR-0775). L0/S4's census (docs/plan/status/386-l0-s4-independent-replay.md) measured the residue at 48 theorem-type-not-prop plus 25 blocked-by-dependency, and named the export change as the natural follow-on."
}