Theorems · Theorem · group theory
LinearOrderedCommGroup.Subgroup.exists_generator_lt_one
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] (H : Subgroup G) [Nontrivial ↥H]
[hH : IsCyclic ↥H], ∃ a < 1, Subgroup.zpowers a = H- Defined in
- Mathlib.Algebra.Order.Group.Cyclic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Subgroupstatement and proof · 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
- lt_trichotomyproof · cited by 178
- IsCyclicstatement and proof · cited by 122
- Subgroup.zpowers_invproof · cited by 11
- Subgroup.nontrivial_iff_ne_botproof · cited by 7
- Left.inv_lt_one_iffproof · cited by 5
- Subgroup.isCyclic_iff_exists_zpowers_eq_topproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- LinearOrderedCommGroup.Subgroup.genLTOneproof · cited by 12
- LinearOrderedCommGroup.Subgroup.genLTOne_zpowers_eq_topproof · cited by 3
- LinearOrderedCommGroup.Subgroup.genLTOne_lt_oneproof · cited by 2