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Theorems · Definition · order theory

Order.Cofinal.above

{P : Type u_1} → [inst : Preorder P] → Order.Cofinal P → P → P

A (noncomputable) element of a cofinal set lying above a given element.

Defined in
Mathlib.Order.Ideal
Cited by
3 results in Mathlib
Foundations
Depth 8 from the axioms · uses Classical.choice
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Order.sequenceOfCofinals.encode_mem · cited by 3sequenceOfCofinals.encode…Order.Cofinal.le_above · cited by 1Cofinal.le_aboveOrder.Cofinal.above_mem · cited by 1Cofinal.above_memPreorder · cited by 7952PreorderOrder.Cofinal · cited by 13Order.CofinalOrder.Cofinal.isCofinal · cited by 2Cofinal.isCofinalCofinal.aboveCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.