Theorems · Theorem · number theory
NumberField.adjoin_eq_top_of_infinitePlace_lt
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : NumberField.RingOfIntegers K}
{w : NumberField.InfinitePlace K},
x ≠ 0 → (∀ ⦃w' : NumberField.InfinitePlace K⦄, w' ≠ w → w' ↑x < 1) → w.IsReal ∨ |(w.embedding ↑x).re| < 1 → ℚ[↑x] = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- absstatement and proof · cited by 1,814
- Subalgebrastatement and proof · cited by 1,353
- Complex.restatement and proof · cited by 882
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement and proof · cited by 604
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