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Theorems · Theorem · order theory

Order.Ideal.IsMaximal.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
2 results in Mathlib
Foundations
Depth 26 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…Order.Ideal.IsMaximal.isCoatom' · cited by 0IsMaximal.isCoatom'IsDirectedOrder · cited by 316IsDirectedOrderIsCoatom · cited by 114IsCoatomOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsMaximal · cited by 8Ideal.IsMaximalOrder.Ideal.ext · cited by 3Ideal.extOrder.Ideal.IsProper.ne_top · cited by 2IsProper.ne_topOrder.Ideal.IsMaximal.maximal_proper · cited by 1IsMaximal.maximal_properIsMaximal.isCoatomCITED 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.