Theorems · Theorem · number theory
denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units
∀ {α : Type u_1} [inst : LinearOrderedCommGroupWithZero α], DenselyOrdered α ↔ Nontrivial αˣ ∧ DenselyOrdered αˣ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- Units.valproof · cited by 1,966
- LT.lt.ne'proof · cited by 1,417
- LT.lt.neproof · cited by 872
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- DenselyOrderedstatement and proof · cited by 471
- Units.mk0proof · cited by 181
- exists_betweenproof · cited by 102
- Ne.isUnitproof · cited by 99
- Units.val_inv_eq_inv_valproof · cited by 57
- eq_zero_or_posproof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- denselyOrdered_units_iffproof · cited by 2