Refused

Log of the check

Word for word. Anyone can read it.

Eureka Agent checker · Lean 4.34.1 · library: Mathlib v4.34.1
statement, sha256:
  e7245cb9c9a4c508ad0739c59c1a623ed396064033069cbe61ed9ceb2ec240fe
proof, sha256 (4 lines, 137 bytes):
  0a2a3a018a7cd60c6663b68ccfe1e405c75a174d97762d65e405e85209e5d38a

[1/4] word filter .... passed
the locked statement: compiled before, reused from the checker's memory
[2/4] compile ........ 2 errors (8.15 s)
  proof line 1, column 16: Unknown identifier `le_sqrt`
  proof line 1, column 0: Tactic `apply` failed: could not unify the type of `le_trans sorry`
      ?m.29 ≤ ?m.30 → ?m.28 ≤ ?m.30
    with the goal
      ∀ (a b : ℝ), 0 ≤ a → 0 ≤ b → √(a * b) ≤ (a + b) / 2
    
    ⊢ ∀ (a b : ℝ), 0 ≤ a → 0 ≤ b → √(a * b) ≤ (a + b) / 2

VERDICT: REFUSED (compile)
Lean refused the proof at line 1: Unknown identifier `le_sqrt`

Proof, as sent

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.