Theorems · Theorem · order theory
Order.cofinal_meets_idealOfCofinals
∀ {P : Type u_1} [inst : Preorder P] (p : P) {ι : Type u_2} [inst_1 : Encodable ι] (𝒟 : ι → Order.Cofinal P) (i : ι),
∃ x ∈ 𝒟 i, x ∈ Order.idealOfCofinals p 𝒟idealOfCofinals p 𝒟 is 𝒟-generic.
- Defined in
- Mathlib.Order.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Encodablestatement and proof · cited by 140
- Encodable.encodeproof · cited by 118
- Order.Idealstatement · cited by 102
- Order.Cofinalstatement and proof · cited by 13
- Order.sequenceOfCofinalsproof · cited by 5
- Order.idealOfCofinalsstatement · cited by 4
- Order.sequenceOfCofinals.encode_memproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Order.iso_of_countable_denseproof · cited by 0
- Order.embedding_from_countable_to_denseproof · cited by 0