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Theorems · Theorem · order theory

Order.Ideal.IsProper.ne_top

∀ {P : Type u_1} [inst : LE P] [inst_1 : IsDirectedOrder P] [inst_2 : Nonempty P] {I : Order.Ideal P},
  I.IsProper → I ≠ ⊤
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.IsMaximal.isCoatom · cited by 2IsMaximal.isCoatomOrder.Ideal.isProper_iff_ne_top · cited by 1Ideal.isProper_iff_ne_topTop.top · cited by 9680Top.topSetLike.coe · cited by 8199SetLike.coeIsDirectedOrder · cited by 316IsDirectedOrderOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsProper · cited by 23Ideal.IsProperOrder.Ideal.IsProper.ne_univ · cited by 1IsProper.ne_univIsProper.ne_topCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.