Theorems · Theorem · order theory
MulArchimedeanClass.subgroup_eq_bot
∀ (M : Type u_1) [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M], MulArchimedeanClass.subgroup ⊤ = ⊥
- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement · cited by 3,593
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- UpperSetstatement · cited by 245
- MulArchimedeanClassstatement · cited by 81
- MulArchimedeanClass.subgroupstatement · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.subgroup_antitoneproof · cited by 1
- MulArchimedeanClass.ballSubgroup_topproof · cited by 0