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Theorems · Theorem · order theory

IsLeast.directedOn

∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderInf α] {s : Set α} {a : α},
  IsLeast s a → DirectedOn (fun x1 x2 => x2 ≤ x1) s
Defined in
Mathlib.Order.ConditionallyCompletePartialOrder.Basic
Cited by
1 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
ConditionallyCompletePartialOrderInf
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Around this declaration

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

IsLeast.csInf_eq · cited by 11IsLeast.csInf_eqSet · cited by 53352SetDirectedOn · cited by 271DirectedOnIsLeast · cited by 122IsLeastConditionallyCompletePartialOrderInf · cited by 51ConditionallyCompletePart…IsLeast.directedOnCITED BYCITES

Cites4

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Cited by1

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