Theorems · Theorem · order theory
LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered
∀ (G : Type u_2) [inst : LinearOrderedCommGroupWithZero G] [Nontrivial Gˣ] [MulArchimedean G], Nonempty (G ≃*o WithZero (Multiplicative ℤ)) ∨ DenselyOrdered G
Any nontrivial (has other than 0 and 1) linearly ordered mul-archimedean group with zero is
either isomorphic (and order-isomorphic) to ℤᵐ⁰, or is densely ordered.
- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- Multiplicativestatement and proof · cited by 875
- WithZerostatement and proof · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- DenselyOrderedstatement · cited by 471
- OrderMonoidIsostatement and proof · cited by 114
- MulArchimedeanstatement and proof · cited by 45
- OrderMonoidIso.symmproof · cited by 44
- OrderMonoidIso.transproof · cited by 11
- OrderMonoidIso.withZeroproof · cited by 6
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