Theorems · Theorem · group theory
LinearOrderedCommGroup.genLTOne_unique
∀ (G : Type u_1) [inst : CommGroup G] [inst_1 : LinearOrder G] [inst_2 : IsOrderedMonoid G] [inst_3 : Nontrivial G]
[inst_4 : IsCyclic G] {g : G}, g < 1 → Subgroup.zpowers g = ⊤ → g = LinearOrderedCommGroup.genLTOne G- Defined in
- Mathlib.Algebra.Order.Group.Cyclic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Subgroupstatement · cited by 3,593
- Nontrivialstatement and proof · cited by 2,416
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- Subgroup.zpowersstatement and proof · cited by 204
- IsCyclicstatement and proof · cited by 122
- LinearOrderedCommGroup.Subgroup.genLTOne_uniqueproof · cited by 5
- LinearOrderedCommGroup.genLTOnestatement · cited by 2
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