What a finite check does establish

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, decided by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.

What a finite check DOES establish, stated exactly: a counterexample cannot be below the bound. That is a real result and it is not the conjecture.

Proposition

∀ n ∈ List.range 1000, holdsBelowAThousand n = true

Proof

By decide in decidability.lean. The kernel reduces the proposition and reports no axiom dependency.

Sources and identifiers

• Lean source · src/pair/formal/proofs/decidability.lean
• Typeset paper · src/research/lean-theorems.tex
• Repository deposit · doi:10.5281/zenodo.21787144
• Author · ORCID 0009-0000-7312-9778
• Deposit record · decidability--what_a_finite_check_does_establish

Proved in the same file

• Verified at every point below the bound
• And false at the bound
• Finite verification does not entail the universal
• A bigger bound proves no more
• The clay files quantify over finite lists

All machine-checked theorems