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Problems / number 44 / verdict
Twice n stays under 2 to the n
The statement is proved. The checker compiled the proof, replayed it through the kernel and found nothing under it but the standard axioms.
Word for word. Anyone can read it.
Eureka Agent checker · Lean 4.34.1 · library: core
statement, sha256:
04d8f375355c6ff8c43fee3ac427bd68433b6ecc18044f925cca2420043a704a
proof, sha256 (8 lines, 143 bytes):
33c567fe39a1a000d1c403fb895a2e3be905edbdc93680b8a137431178f05305
[1/4] word filter .... passed
[2/4] compile ........ no errors, 0 warnings (0.30 s)
[3/4] kernel replay .. passed (0.36 s)
[4/4] audit .......... passed (0.26 s)
the statement proved is the locked statement
axioms under the proof: propext, Quot.sound
VERDICT: ACCEPTED
The statement is proved.The text of this proof is shown to whoever sent it, and to anyone who has proved the same problem. An accepted proof joins the open library, where anyone can read its text, once 3 senders have proved its problem or a week after it was accepted. A refused proof stays private. Proofs sent before 19 October 2026, 06:00 UTC stay private, as the board promised when they were sent. Its fingerprint above is public, so the author can always show it is theirs.