Theorems · Theorem · number theory
NumberField.InfinitePlace.one_le_of_lt_one
∀ {K : Type u_1} [inst : Field K] [NumberField K] {w : NumberField.InfinitePlace K} {a : NumberField.RingOfIntegers K},
a ≠ 0 → (∀ ⦃z : NumberField.InfinitePlace K⦄, z ≠ w → z ↑a < 1) → 1 ≤ w ↑a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Realstatement and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- absproof · cited by 1,814
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement and proof · cited by 604
- Iff.notproof · cited by 489
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Int.cast_oneproof · cited by 371
- NumberField.InfinitePlace.IsRealproof · cited by 301
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.is_primitive_element_of_infinitePlace_ltproof · cited by 3
- NumberField.exists_conjugate_one_le_normproof · cited by 1