Theorems · Definition · order theory
FiniteArchimedeanClass.toUpperSetAddArchimedeanClass
{M : Type u_1} →
[inst : AddCommGroup M] →
[inst_1 : LinearOrder M] →
[inst_2 : IsOrderedAddMonoid M] → UpperSet (FiniteArchimedeanClass M) ↪o UpperSet (ArchimedeanClass M)The upper set in ArchimedeanClass M consisting of an upper set in
FiniteArchimedeanClass M plus ⊤.
- 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.
Cites10
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
- Set.ofPredproof · cited by 6,101
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- OrderEmbeddingstatement · cited by 619
- ArchimedeanClassstatement and proof · cited by 247
- UpperSetstatement and proof · cited by 245
- FiniteArchimedeanClassstatement and proof · cited by 100
- OrderEmbedding.ofStrictMonoproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- FiniteArchimedeanClass.addSubgroupproof · cited by 4
- FiniteArchimedeanClass.addSubgroup_strictAntiproof · cited by 2
- FiniteArchimedeanClass.addSubgroup_eq_botproof · cited by 0
- FiniteArchimedeanClass.subsemigroup_eq_addSubgroupstatement · cited by 0