Theorems · Theorem · group theory
LinearOrderedCommGroup.Subgroup.genLTOne_lt_one
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [inst_2 : IsOrderedMonoid G] (H : Subgroup G)
[inst_3 : Nontrivial ↥H] [hH : IsCyclic ↥H], LinearOrderedCommGroup.Subgroup.genLTOne H < 1- Defined in
- Mathlib.Algebra.Order.Group.Cyclic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsCyclicstatement and proof · cited by 122
- LinearOrderedCommGroup.Subgroup.genLTOnestatement · cited by 12
- LinearOrderedCommGroup.Subgroup.exists_generator_lt_oneproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- LinearOrderedCommGroup.Subgroup.genLTOne_uniqueproof · cited by 5
- Valuation.exists_isUniformizer_of_isCyclic_of_nontrivialproof · cited by 2