Theorems · Theorem · order theory
Order.Ideal.exists_maximal
∀ {P : Type u_1} [inst : PartialOrder P] [OrderTop P] [Nontrivial P], ∃ I, I.IsMaximal- Defined in
- Mathlib.Order.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialstatement and proof · cited by 2,416
- OrderTopstatement and proof · cited by 493
- Order.Idealstatement and proof · cited by 102
- exists_neproof · cited by 101
- Order.Ideal.principalproof · cited by 12
- Order.Ideal.IsMaximalstatement and proof · cited by 8
- Order.Ideal.isProper_principal_iffproof · cited by 1
- Order.Ideal.IsProper.exists_le_maximalproof · cited by 1
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