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Theorems · Theorem · order theory

Order.Ideal.isProper_of_ne_top

∀ {P : Type u_1} [inst : LE P] [inst_1 : IsDirectedOrder P] [inst_2 : Nonempty P] {I : Order.Ideal P},
  I ≠ ⊤ → I.IsProper
Defined in
Mathlib.Order.Ideal
Cited by
2 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
LEIsDirectedOrderNonempty
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.Ideal.isProper_iff_ne_top · cited by 1Ideal.isProper_iff_ne_topIsCoatom.isProper · cited by 1IsCoatom.isProperTop.top · cited by 9680Top.topSetLike.coe · cited by 8199SetLike.coeSet.univ · cited by 3945Set.univIsDirectedOrder · cited by 316IsDirectedOrderOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsProper · cited by 23Ideal.IsProperOrder.Ideal.ext · cited by 3Ideal.extIdeal.isProper_of_ne_topCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.