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Theorems · Definition · order theory

FiniteArchimedeanClass.ballAddSubgroup

{M : Type u_1} →
  [inst : AddCommGroup M] →
    [inst_1 : LinearOrder M] → [inst_2 : IsOrderedAddMonoid M] → FiniteArchimedeanClass M → AddSubgroup M

An open ball defined by FiniteArchimedeanClass.addSubgroup of UpperSet.Ioi c.

Defined in
Mathlib.Algebra.Order.Archimedean.Class
Cited by
3 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupLinearOrderIsOrderedAddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FiniteArchimedeanClass.ballAddSubgroup_strictAnti · cited by 1FiniteArchimedeanClass.ba…FiniteArchimedeanClass.mem_ballAddSubgroup_iff · cited by 1FiniteArchimedeanClass.me…FiniteArchimedeanClass.toAddSubgroup_ball · cited by 0FiniteArchimedeanClass.to…AddCommGroup · cited by 12871AddCommGroupLinearOrder · cited by 8572LinearOrderAddSubgroup · cited by 3232AddSubgroupIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidFiniteArchimedeanClass · cited by 100FiniteArchimedeanClassUpperSet.Ioi · cited by 15UpperSet.IoiFiniteArchimedeanClass.addSubgroup · cited by 4FiniteArchimedeanClass.ad…FiniteArchimedeanClass.ballAd…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.