Theorems · Theorem · order theory
Order.Ideal.lower
∀ {P : Type u_1} [inst : LE P] (s : Order.Ideal P), IsLowerSet ↑s- Defined in
- Mathlib.Order.Ideal
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- IsLowerSetstatement · cited by 167
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.toLowerSetproof · cited by 9
- LowerSet.lower'proof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- Order.Ideal.sup_memproof · cited by 5
- Order.PFilter.mem_of_leproof · cited by 3
- Order.Ideal.top_mem_iff_eq_topproof · cited by 3
- Order.Ideal.isIdealproof · cited by 3
- Order.Ideal.bot_memproof · cited by 2
- Order.Ideal.sup_mem_iffproof · cited by 1
- Order.Ideal.isPrime_of_mem_or_compl_memproof · cited by 1
- Order.Ideal.eq_sup_of_le_supproof · cited by 1
- Order.Ideal.mem_compl_of_geproof · cited by 1
- Order.Ideal.principal_le_iffproof · cited by 1
- Order.Ideal.inter_nonemptyproof · cited by 0