Theorems · Definition · order theory
Order.Ideal.principal
{P : Type u_1} → [inst : Preorder P] → P → Order.Ideal PThe smallest ideal containing a given element.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- LowerSetproof · cited by 230
- Order.Idealstatement · cited by 102
- LowerSet.Iicproof · cited by 37
- Set.nonempty_Iicproof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- Order.PFilter.principalproof · cited by 5
- Lattice.mem_ideal_sup_principalstatement and proof · cited by 2
- Order.Ideal.mem_principalstatement · cited by 2
- Order.Ideal.isProper_principal_iffstatement · cited by 1
- Order.Ideal.mem_principal_selfstatement · cited by 1
- Order.Ideal.principal_le_iffstatement and proof · cited by 1
- DistribLattice.prime_ideal_of_disjoint_filter_idealproof · cited by 0
- Order.Ideal.exists_maximalproof · cited by 0
- Order.Ideal.lt_sup_principal_of_notMemstatement and proof · cited by 0
- Order.Ideal.principal_botstatement · cited by 0
- Order.Ideal.principal_toLowerSetstatement and proof · cited by 0
- Order.Ideal.principal_topstatement and proof · cited by 0