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exists_semiring_unique_left_right_maximal_ne

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There exists a semiring with a unique left maximal ideal and a unique right maximal ideal which are not the same as sets.

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Lean 4 Statement 
theorem exists_semiring_unique_left_right_maximal_ne :
    answer(sorry) ↔ ∃ (R : Type) (_ : Semiring R) (hI : ∃! I : Ideal R, I.IsMaximal)
      (hJ : ∃! J : Ideal Rᵐᵒᵖ, J.IsMaximal),
        (hI.choose : Set R) ≠ MulOpposite.op ⁻¹' hJ.choose
ID: Mathoverflow__486451__exists_semiring_unique_left_right_maximal_ne
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