Theorems · Theorem · order theory
FiniteArchimedeanClass.mem_ballAddSubgroup_iff
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M}
{c : FiniteArchimedeanClass M}, a ∈ c.ballAddSubgroup ↔ ∀ (h : a ≠ 0), c < FiniteArchimedeanClass.mk a h- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · 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
- FiniteArchimedeanClassstatement and proof · cited by 100
- FiniteArchimedeanClass.mkstatement and proof · cited by 28
- FiniteArchimedeanClass.ballAddSubgroupstatement · cited by 3
- UpperSet.mem_Ioi_iffproof · cited by 2
- FiniteArchimedeanClass.mem_addSubgroup_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- FiniteArchimedeanClass.mem_ball_iffproof · cited by 2