Theorems · Theorem · order theory
Order.Ideal.principal_le_iff
∀ {P : Type u_1} [inst : Preorder P] {I : Order.Ideal P} {x : P}, Order.Ideal.principal x ≤ I ↔ x ∈ I- Defined in
- Mathlib.Order.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- 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
- le_rflproof · cited by 1,558
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.principalstatement and proof · cited by 12
- Order.Ideal.lowerproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Order.PFilter.principal_le_iffproof · cited by 0