Mathlib Map

Theorems · Definition · order theory

UpperSet.Ioi

{α : Type u_1} → [inst : Preorder α] → α → UpperSet α

Strict principal upper set. Set.Ioi as an upper set.

Defined in
Mathlib.Order.UpperLower.Principal
Cited by
15 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FiniteArchimedeanClass.ball · cited by 23FiniteArchimedeanClass.ba…UpperSet.Ioi_strictMono · cited by 4UpperSet.Ioi_strictMonoFiniteArchimedeanClass.ballAddSubgroup · cited by 3FiniteArchimedeanClass.ba…ArchimedeanClass.ballAddSubgroup · cited by 3ArchimedeanClass.ballAddS…MulArchimedeanClass.ballSubgroup · cited by 3MulArchimedeanClass.ballS…UpperSet.mem_Ioi_iff · cited by 2UpperSet.mem_Ioi_iffFiniteMulArchimedeanClass.ballSubgroup · cited by 2FiniteMulArchimedeanClass…UpperSet.Ioi_top · cited by 2UpperSet.Ioi_topFiniteArchimedeanClass.ballAddSubgroup_strictAnti · cited by 1FiniteArchimedeanClass.ba…FiniteArchimedeanClass.ball_lt_closedBall · cited by 1FiniteArchimedeanClass.ba…UpperSet.Ioi_eq_top · cited by 1UpperSet.Ioi_eq_topHahnEmbedding.Partial.eval_eq_truncLT · cited by 1Partial.eval_eq_truncLTUpperSet.map_Ioi · cited by 0UpperSet.map_IoiUpperSet.Ici_le_Ioi · cited by 0UpperSet.Ici_le_IoiArchimedeanClass.ballAddSubgroup_antitone · cited by 0ArchimedeanClass.ballAddS…Preorder · cited by 7952PreorderSet.Ioi · cited by 1463Set.IoiUpperSet · cited by 245UpperSetisUpperSet_Ioi · cited by 1isUpperSet_IoiUpperSet.IoiCITED BYCITES

Cites4

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

Cited by20

Results whose statement or proof uses this declaration.