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Theorems · Definition · order theory

Order.Ideal.IsMaximal.casesOn

{P : Type u_1} →
  [inst : LE P] →
    {I : Order.Ideal P} →
      {motive : I.IsMaximal → Sort u} →
        (t : I.IsMaximal) →
          ([toIsProper : I.IsProper] → (maximal_proper : ∀ ⦃J : Order.Ideal P⦄, I < J → ↑J = Set.univ) → motive ⋯) →
            motive t
Defined in
Mathlib.Order.Ideal
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
LE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Order.Ideal.isMaximal_iff · cited by 0Ideal.isMaximal_iffSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSet.univ · cited by 3945Set.univOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsProper · cited by 23Ideal.IsProperOrder.Ideal.IsMaximal · cited by 8Ideal.IsMaximalIsMaximal.casesOnCITED 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.