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Theorems · Theorem · order theory

le_csSup_iff

∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α},
  BddAbove s → s.Nonempty → (a ≤ sSup s ↔ ∀ b ∈ upperBounds s, a ≤ b)
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
ConditionallyCompleteLattice
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Around this declaration

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

Archimedean.embedRealFun_zero · cited by 0Archimedean.embedRealFun_…Archimedean.embedReal_one · cited by 0Archimedean.embedReal_oneSet · cited by 53352SetSet.Nonempty · cited by 2627Set.Nonemptyle_trans · cited by 985le_transSupSet.sSup · cited by 954SupSet.sSupBddAbove · cited by 620BddAboveConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…upperBounds · cited by 263upperBoundsle_csSup · cited by 66le_csSupcsSup_le · cited by 35csSup_lele_csSup_iffCITED BYCITES

Cites9

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Cited by2

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