Theorems · Theorem · order theory
ArchimedeanClass.mem_addSubgroup_iff
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M}
{s : UpperSet (ArchimedeanClass M)}, s ≠ ⊤ → (a ∈ ArchimedeanClass.addSubgroup s ↔ ArchimedeanClass.mk a ∈ s)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 3 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.
Cites16
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
- SetLike.coeproof · cited by 8,199
- Set.preimageproof · cited by 4,946
- AddSubgroupstatement · cited by 3,232
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- SetLike.mem_coeproof · cited by 302
- ArchimedeanClassstatement and proof · cited by 247
- UpperSetstatement and proof · cited by 245
- Set.mem_preimageproof · cited by 190
- ArchimedeanClass.mkstatement and proof · cited by 174
Cited by3
Results whose statement or proof uses this declaration.
- ArchimedeanClass.closedBallAddSubgroup_topproof · cited by 0
- ArchimedeanClass.mem_ballAddSubgroup_iffproof · cited by 0
- ArchimedeanClass.mem_closedBallAddSubgroup_iffproof · cited by 0