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Problems / number 26 / verdict
Powers of two outrun the exponent
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:
fb2ceb30e4d1d941d8da37ecc64d0eb92075ddc944fa23f512dc0d8205b0ccf4
proof, sha256 (4 lines, 81 bytes):
00a176dca0d0cc4fe71881d05ee73edefca2916c98d30dbe7163db759fea5967
[1/4] word filter .... passed
[2/4] compile ........ no errors, 0 warnings (0.31 s)
[3/4] kernel replay .. passed (0.34 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.