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Theorems · Theorem · order theory

IsCoatom.isProper

∀ {P : Type u_1} [inst : LE P] [inst_1 : IsDirectedOrder P] [inst_2 : Nonempty P] {I : Order.Ideal P},
  IsCoatom I → I.IsProper
Defined in
Mathlib.Order.Ideal
Cited by
1 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.

IsCoatom.isMaximal · cited by 1IsCoatom.isMaximalIsDirectedOrder · cited by 316IsDirectedOrderIsCoatom · cited by 114IsCoatomOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsProper · cited by 23Ideal.IsProperOrder.Ideal.isProper_of_ne_top · cited by 2Ideal.isProper_of_ne_topIsCoatom.isProperCITED BYCITES

Cites5

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.