Theorems · Theorem · order theory
not_isCyclic_of_denselyOrdered
∀ (α : Type u_1) [inst : CommGroup α] [inst_1 : LinearOrder α] [IsOrderedMonoid α] [DenselyOrdered α] [Nontrivial α], ¬IsCyclic α
A nontrivial densely linear ordered commutative group can't be a cyclic group.
- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Nontrivialstatement and proof · cited by 2,416
- pow_zeroproof · cited by 1,094
- CommGroupstatement and proof · cited by 990
- pow_oneproof · cited by 894
- IsOrderedMonoidstatement and proof · cited by 577
- DenselyOrderedstatement and proof · cited by 471
- zpow_negproof · cited by 198
- lt_trichotomyproof · cited by 178
- zpow_ofNatproof · cited by 144
- IsCyclicstatement and proof · cited by 122
- exists_betweenproof · cited by 102
Cited by1
Results whose statement or proof uses this declaration.
- not_denseRange_zpowproof · cited by 1