Theorems · Definition · order theory
ArchimedeanClass.addSubgroup
{M : Type u_1} →
[inst : AddCommGroup M] →
[inst_1 : LinearOrder M] → [inst_2 : IsOrderedAddMonoid M] → UpperSet (ArchimedeanClass M) → AddSubgroup MMake ArchimedeanClass.subsemigroup a subgroup by assigning
s = ⊤ with a junk value ⊥.
- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 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.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Bot.botproof · cited by 4,720
- AddSubgroupstatement · cited by 3,232
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- AddSubsemigroupproof · cited by 262
- ArchimedeanClassstatement and proof · cited by 247
- UpperSetstatement and proof · cited by 245
- ArchimedeanClass.subsemigroupproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mem_addSubgroup_iffstatement · cited by 3
- ArchimedeanClass.ballAddSubgroupproof · cited by 3
- ArchimedeanClass.addSubgroup_eq_botstatement · cited by 2
- ArchimedeanClass.closedBallAddSubgroupproof · cited by 2
- ArchimedeanClass.addSubgroup_antitonestatement and proof · cited by 1
- ArchimedeanClass.addSubgroup_strictAntiOnstatement and proof · cited by 1
- ArchimedeanClass.subsemigroup_eq_addSubgroup_of_ne_topstatement · cited by 1
- ArchimedeanClass.ballAddSubgroup_topproof · cited by 0