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Theorems · Theorem · order theory

Order.Ideal.isMaximal_iff_isCoatom

∀ {P : Type u_1} [inst : LE P] [inst_1 : IsDirectedOrder P] [inst_2 : Nonempty P] {I : Order.Ideal P},
  I.IsMaximal ↔ IsCoatom I
Defined in
Mathlib.Order.Ideal
Cited by
1 results in Mathlib
Foundations
Depth 28 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.exists_le_maximal · cited by 1IsProper.exists_le_maximalIsDirectedOrder · cited by 316IsDirectedOrderIsCoatom · cited by 114IsCoatomOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsMaximal · cited by 8Ideal.IsMaximalOrder.Ideal.IsMaximal.isCoatom · cited by 2IsMaximal.isCoatomIsCoatom.isMaximal · cited by 1IsCoatom.isMaximalIdeal.isMaximal_iff_isCoatomCITED BYCITES

Cites6

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.