Theorems · Theorem · order theory
ArchimedeanClass.subsemigroup_eq_addSubgroup_of_ne_top
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M]
{s : UpperSet (ArchimedeanClass M)}, s ≠ ⊤ → ↑(ArchimedeanClass.subsemigroup s) = ↑(ArchimedeanClass.addSubgroup s)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- AddSubgroupstatement · cited by 3,232
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- AddSubsemigroupstatement · cited by 262
- ArchimedeanClassstatement and proof · cited by 247
- UpperSetstatement and proof · cited by 245
- ArchimedeanClass.addSubgroupstatement · cited by 6
- ArchimedeanClass.subsemigroupstatement and proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- ArchimedeanClass.addSubgroup_strictAntiOnproof · cited by 1