FormalConjectures/Mathoverflow/21003.lean

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Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL
Lean4 Domain Explanation Language

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Mathoverflow 21003

Is there any polynomial $f(x, y) \in \mathbb{Q}[x, y]$ such that $f : \mathbb{Q} \times \mathbb{Q} \rightarrow \mathbb{Q}$ is a bijection?

Reference: mathoverflow/21003 asked by user Z.H.

Imports (1)
  1. theorem Mathoverflow21003.mathoverflow_21003 Is there any polynomial $f(x, y) \in \mathbb{Q}[x, y]$ such that $f : \mathbb{Q} \times \mathbb{Q} \rightarrow \mathbb{Q}$ is a bijection? sorry line 42 source

    Source documentation

    Is there any polynomial $f(x, y) \in \mathbb{Q}[x, y]$ such that $f : \mathbb{Q} \times \mathbb{Q} \rightarrow \mathbb{Q}$ is a bijection?

    depends on sorry what this means

    Statement uses: Iff, True, Exists, MvPolynomial, Fin, OfNat.ofNat, Nat, Rat, Function.Bijective, RingHom, Finsupp, MvPolynomial.eval

    Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous

    24 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

    theorem mathoverflow_21003 :
    answer(sorry) ↔ ∃ f : MvPolynomial (Fin 2) ℚ, Function.Bijective fun x ↦ f.eval x := by
…