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Theorems · Theorem · order theory

IsCoatom.isMaximal

∀ {P : Type u_1} [inst : LE P] [inst_1 : IsDirectedOrder P] [inst_2 : Nonempty P] {I : Order.Ideal P},
  IsCoatom I → I.IsMaximal
Defined in
Mathlib.Order.Ideal
Cited by
1 results in Mathlib
Foundations
Depth 27 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_iff_isCoatom · cited by 1Ideal.isMaximal_iff_isCoa…SetLike.coe · cited by 8199SetLike.coeSet.univ · cited by 3945Set.univIsDirectedOrder · cited by 316IsDirectedOrderIsCoatom · cited by 114IsCoatomOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsProper · cited by 23Ideal.IsProperOrder.Ideal.IsMaximal · cited by 8Ideal.IsMaximalIsCoatom.isProper · cited by 1IsCoatom.isProperIsCoatom.isMaximalCITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.