Theorems · Theorem · order theory
FiniteArchimedeanClass.mem_ball_iff
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] (K : Type u_2)
[inst_3 : Ring K] [inst_4 : LinearOrder K] [inst_5 : IsOrderedRing K] [inst_6 : Archimedean K] [inst_7 : Module K M]
[inst_8 : PosSMulMono K M] {a : M} {c : FiniteArchimedeanClass M},
a ∈ FiniteArchimedeanClass.ball K c ↔ ∀ (h : a ≠ 0), c < FiniteArchimedeanClass.mk a h- Defined in
- Mathlib.Algebra.Order.Module.Archimedean
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- IsOrderedRingstatement and proof · cited by 777
- Archimedeanstatement and proof · cited by 603
- ArchimedeanClassstatement · cited by 247
- PosSMulMonostatement and proof · cited by 188
- FiniteArchimedeanClassstatement and proof · cited by 100
Cited by2
Results whose statement or proof uses this declaration.
- HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratumproof · cited by 3
- HahnEmbedding.Partial.eval_neproof · cited by 1