Theorems · Theorem · number theory
NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrank
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K],
Odd (Module.finrank ℚ K) → ∀ (x : ↥(NumberField.Units.torsion K)), ↑x = 1 ∨ ↑x = -1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 298 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- le_antisymmproof · cited by 2,068
- Units.valproof · cited by 1,966
- Nat.cast_zeroproof · cited by 1,870
- Module.finrankstatement and proof · cited by 1,770
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Oddstatement and proof · cited by 364
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.Units.torsionOrder_eq_two_of_odd_finrankproof · cited by 0