Theorems · Theorem · order theory
ArchimedeanClass.mem_ballAddSubgroup_iff
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M}
{c : ArchimedeanClass M}, c ≠ ⊤ → (a ∈ c.ballAddSubgroup ↔ c < ArchimedeanClass.mk a)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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 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 and proof · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.ballAddSubgroupstatement · cited by 3
- ArchimedeanClass.mem_addSubgroup_iffproof · cited by 3
- UpperSet.mem_Ioi_iffproof · cited by 2
- UpperSet.Ioi_eq_topproof · cited by 1
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