the ten digits are two fixed points and four pairs

lean

theorem the_ten_digits_are_two_fixed_points_and_four_pairs :
  (digits.filter (fun d => tv d == d)).length = 2 ∧ (digits.filter (fun d => tv d != d)).length = 8 ∧ 2 + 4 * 2 = 10

Accepted by the Lean 4 kernel. The proof rests on no axioms at all.

Proven means three things together: the kernel accepted the file, the proof contains no sorry, and #print axioms reports a dependency set within {propext, Quot.sound}. The dependency set above is the evidence, recorded per theorem rather than summarised.


source	`lean/DigitSpace.lean:193`
archive	doi:10.5281/zenodo.22178675 — the concept DOI, resolving to the newest release
corpus	every statement · the ledger
reproduce	`git clone https://github.com/ceccec/zeropoint-node && npm run lean:check`

Speaks of the same objects as

What this does not establish

A theorem is a statement the kernel accepted. It says nothing about whether the surrounding package is useful, whether the idea is novel, or whether anything physical follows. Novelty is a universal negative no finite search decides; a dated deposit establishes priority, which is the defensible claim.

the ten digits are two fixed points and four pairs ​

Speaks of the same objects as ​

the ten digits are two fixed points and four pairs

Speaks of the same objects as