Identifier
F:evt-mathlib-import-compact-exists-is-max-on
Proof route
imported-kernel-lean
External status
proved
Axiom footprint
lean4export-3.1.0-stream-faithfulness, axeyum-lean-import-wire-translation, lean4export-3.1.0-delivered-bytes-are-the-intended-export, Classical.choice, Quot, Quot.lift, Quot.mk, Quot.sound, String.Internal.append, propext, wrapped._@.Mathlib.Topology.Defs.Filter.2998874748._hygCtx._hyg.2

Recorded description

The proposition Mathlib states as IsCompact.exists_isMaxOn: for a nonempty compact set s in a topological space and f continuous on s into a linear order with closed Ici topology, there exists x in s attaining the maximum of f on s. Imported as Mathlib's own statement and proof term, not established by this project -- see proof_route.

Formal statement
((α : Sort (u_2+1)) -> ((β : Sort (u_3+1)) -> ((inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._6 : LinearOrder.{u_2} α) -> ((inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._9 : TopologicalSpace.{u_2} α) -> ((inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._12 : TopologicalSpace.{u_3} β) -> ((inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._18 : ClosedIciTopology.{u_2} α inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._9 (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._6)))))) -> ((s : Set.{u_3} β) -> ((hs : IsCompact.{u_3} β inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._12 s) -> ((ne_s : Set.Nonempty.{u_3} β s) -> ((f : ((a._@._internal._hyg._0 : β) -> α)) -> ((hf : ContinuousOn.{u_3, u_2} β α inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._12 inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._9 f s) -> Exists.{u_3+1} β (fun (x : β) => And (Membership.mem.{u_3, u_3} β (Set.{u_3} β) (Set.instMembership.{u_3} β) s x) (IsMaxOn.{u_3, u_2} β α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Topology.Order.Compact._3966579681._hygCtx._hyg._6))))) f s x)))))))))))))

Dependencies

The graph shows direct ledger edges. Follow a node to open its artifact page.

Direct dependencies appear to the left. The current fact is in the center. Facts that depend directly on it appear to the right. Current fact
0 direct dependencies 0 direct dependents

Evidence

import-IsCompact.exists_isMaxOn

Kind
kernel-term
Status
checked

Supports: `IsCompact.exists_isMaxOn`'s Lean proof term type-checks against this statement in the independent Axeyum kernel.

Checker command
test "$(cargo test -p axeyum-lean-import --test imported_fact_evidence -- --nocapture 2>/dev/null | grep -c 'AXEYUM-IMPORT-FACT|F:evt-mathlib-import-compact-exists-is-max-on|')" -ge 1
Evidence notes

The command greps for this fact's own marker line rather than trusting the exit status, so a suite that compiles to zero tests -- this repository's signature defect -- fails instead of exiting 0. `lean4export_census` reports 2171 declaration records / 2486 admitted declarations for the transitive dependency closure of `IsCompact.exists_isMaxOn` at Mathlib commit c5ea00351c28e24afc9f0f84379aa41082b1188f (module: see MANIFEST.json), all admitted by `Kernel::add_declaration` with ZERO declines. `Kernel::render_lean` of the admitted type is `formal.statement` verbatim. the constructive substitute (approximate, non-attaining) is F:creal-evt-approx-max (row 1), the boundary reduction is F:creal-evt-attained-max-decides-sign (row 2).

footprint-IsCompact.exists_isMaxOn

Kind
exhaustive-enumeration
Status
checked

Supports: axiom_footprint: the imported proof term's trusted-declaration footprint inside the imported environment, plus the three import-route assumptions this route always carries.

Checker command
scripts/check-imported-fact-lean-axioms.sh "IsCompact.exists_isMaxOn"
Evidence notes

`Kernel::axiom_footprint` over the imported environment reports [Classical.choice, Quot, Quot.lift, Quot.mk, Quot.sound, String.Internal.append, propext, wrapped._@.Mathlib.Topology.Defs.Filter.2998874748._hygCtx._hyg.2] -- eight names, not Lean's own three (`#print axioms` reports [propext, Classical.choice, Quot.sound] for both theorems at this pinned commit, per docs/formalized-math-2026-08/08-ivt-and-evt-measured-against-mathlib.md section 3). The extra five are this kernel's finer-grained classification of the Quotient package (Quot itself, Quot.lift and Quot.mk alongside Quot.sound -- documented in fact.schema.json's proof_route field as 'must not be silently reconciled to Lean's'), plus two names this specific dependency closure reaches that the three hand-picked Init/Std imports never did: a String.Internal.append opaque and a wrapped._@.Mathlib.Topology.Defs.Filter opaque wrapper from a well-founded-recursion definition somewhere in the Filter machinery both theorems' proofs transitively use. Neither is a defect in the translation; both are real trusted declarations Mathlib's own proof rests on for this statement, and Kernel::axiom_footprint is reporting them faithfully. The first three entries in this array are the assumptions the IMPORT ROUTE adds on top: that the exporter faithfully rendered Lean's environment, that this crate's NDJSON-to-kernel-term translation preserves meaning, and that the delivered bytes are the producer's intended export (format 3.1 has no footer, so completion is relative to the bytes handed over).

Provenance

{
  "date": "2026-08-31",
  "established_by": "axeyum-lean-import, lane row4-labeled-import -- our independent kernel ADMITTED Mathlib's proof term, together with the whole transitive dependency closure the export pulled in. This project did NOT construct the proof; see proof_route. This is ADR-0603 row 4 (labeled import) for this statement family.",
  "source": "official lean4export NDJSON 3.1.0 stream artifacts/lean-imports/evt-is-compact-exists-is-max-on.ndjson, declaration `IsCompact.exists_isMaxOn` from mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f under Lean 4.30.0",
  "prior_art": [
    {
      "who": "the Mathlib community",
      "what": "`IsCompact.exists_isMaxOn` in mathlib4",
      "where": "leanprover-community/mathlib4, commit c5ea00351c28e24afc9f0f84379aa41082b1188f",
      "year": 2026,
      "attribution": "read directly from the pinned lean4export stream this fact cites, and independently admitted by Kernel::add_declaration; this lane did not consult a paper or a secondary source."
    }
  ]
}