Theorems · Theorem · order theory

DirectedOn.csInf_le_csInf

∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderInf α] {s t : Set α},
  DirectedOn (fun x1 x2 => x2 ≤ x1) s →
    DirectedOn (fun x1 x2 => x2 ≤ x1) t → BddBelow t → s.Nonempty → s ⊆ t → sInf t ≤ sInf s

Defined in: Mathlib.Order.ConditionallyCompletePartialOrder.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 10 from the axioms · uses no axioms
Assumes: ConditionallyCompletePartialOrderInf

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Setstatement and proof · cited by 53,352
Set.Nonemptystatement and proof · cited by 2,627
InfSet.sInfstatement · cited by 935
BddBelowstatement and proof · cited by 401
DirectedOnstatement and proof · cited by 271
ConditionallyCompletePartialOrderInfstatement and proof · cited by 51
DirectedOn.csInf_leproof · cited by 9
DirectedOn.le_csInfproof · cited by 4

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