Theorems · Theorem · order theory
not_isAddCyclic_of_denselyOrdered
∀ (α : Type u_1) [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] [DenselyOrdered α] [Nontrivial α], ¬IsAddCyclic α
A nontrivial densely linear ordered additive 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Nontrivialstatement and proof · cited by 2,416
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- DenselyOrderedstatement and proof · cited by 471
- lt_trichotomyproof · cited by 178
- zero_nsmulproof · cited by 137
- exists_betweenproof · cited by 102
- exists_neproof · cited by 101
- neg_posproof · cited by 74
- one_nsmulproof · cited by 63
- IsAddCyclicstatement and proof · cited by 55
Cited by1
Results whose statement or proof uses this declaration.
- not_denseRange_zsmulproof · cited by 2