Theorems · Theorem · order theory
FiniteArchimedeanClass.mem_addSubgroup_iff
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M}
{s : UpperSet (FiniteArchimedeanClass M)},
a ∈ FiniteArchimedeanClass.addSubgroup s ↔ ∀ (h : a ≠ 0), FiniteArchimedeanClass.mk a h ∈ s- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- AddSubgroupstatement · cited by 3,232
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- UpperSetstatement and proof · cited by 245
- ArchimedeanClass.mkproof · cited by 174
- FiniteArchimedeanClassstatement and proof · cited by 100
- FiniteArchimedeanClass.mkstatement · cited by 28
- ArchimedeanClass.mk_eq_top_iffproof · cited by 7
- FiniteArchimedeanClass.addSubgroupstatement and proof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- FiniteArchimedeanClass.mem_ballAddSubgroup_iffproof · cited by 1
- FiniteArchimedeanClass.mem_closedBallAddSubgroup_iffproof · cited by 1