Theorems · Theorem · group theory
LinearOrderedCommGroup.Subgroup.genLTOne_unique_of_zpowers_eq
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] {g1 g2 : G},
g1 < 1 → g2 < 1 → Subgroup.zpowers g1 = Subgroup.zpowers g2 → g1 = g2- 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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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
- Bot.botproof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Nontrivialproof · cited by 2,416
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- Subgroup.zpowersstatement and proof · cited by 204
- IsCyclicproof · cited by 122
- LinearOrderedCommGroup.Subgroup.genLTOneproof · cited by 12
- LinearOrderedCommGroup.Subgroup.genLTOne_uniqueproof · cited by 5
- Subgroup.isCyclic_iff_exists_zpowers_eq_topproof · cited by 4
- Subgroup.bot_or_nontrivialproof · cited by 3
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