Schanuel.lean`

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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

Schanuel's Conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

theorem Schanuel.schanuel_conjecture Documented declaration: schanuel_conjecture sorry line 39 source
Source documentation
Given any set of $n$ complex numbers $\{z_1, ..., z_n\}$ that are linearly independent over $\mathbb{Q}$, the field extension $\mathbb{Q}(z_1, ..., z_n, e^{z_1}, ..., e^{z_n})$ has transcendence degree at least $n$ over $\mathbb{Q}$.

depends on sorry what this means
Statement uses: Nat, Fin, Complex, LinearIndependent, Rat, LE.le, Cardinal, Algebra.trdeg, Subtype, Membership.mem, IntermediateField, IntermediateField.adjoin, Union.union, Set, Set.range, Function.comp, Complex.exp
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
67 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem schanuel_conjecture (n : ℕ) (z : Fin n → ℂ) (h : LinearIndependent ℚ z) :
    n ≤ Algebra.trdeg ℚ (adjoin ℚ (Set.range z ∪ Set.range (cexp ∘ z))) := by
…
```