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Theorems · Theorem · order theory

PrincipalSeg.lt_top

∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (f : PrincipalSeg r s) (a : α),
  s (f.toRelEmbedding a) f.top
Defined in
Mathlib.Order.InitialSeg
Cited by
7 results in Mathlib
Foundations
Depth 14 from the axioms · uses no axioms
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Around this declaration

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

PrincipalSeg.mem_range_of_rel · cited by 24PrincipalSeg.mem_range_of…Ordinal.typein_lt_type · cited by 13Ordinal.typein_lt_typeCardinal.lift_lt_univ · cited by 2Cardinal.lift_lt_univCategoryTheory.Limits.hasColimitsOfShape_of_initialSeg · cited by 1Limits.hasColimitsOfShape…PrincipalSeg.top_rel_top · cited by 0PrincipalSeg.top_rel_topPrincipalSeg.subrelIso_apply · cited by 0PrincipalSeg.subrelIso_ap…PrincipalSeg.irrefl · cited by 0PrincipalSeg.irreflDFunLike.coe · cited by 62936DFunLike.coeRelEmbedding · cited by 281RelEmbeddingPrincipalSeg.toRelEmbedding · cited by 129PrincipalSeg.toRelEmbeddi…PrincipalSeg · cited by 73PrincipalSegPrincipalSeg.top · cited by 41PrincipalSeg.topPrincipalSeg.mem_range_iff_rel · cited by 5PrincipalSeg.mem_range_if…PrincipalSeg.lt_topCITED BYCITES

Cites6

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

Cited by7

Results whose statement or proof uses this declaration.