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Theorems · Theorem · order theory

ConditionallyCompleteLattice.isLUB_csSup

∀ {α : Type u_5} [self : ConditionallyCompleteLattice α] (s : Set α), s.Nonempty → BddAbove s → IsLUB s (sSup s)

Every nonempty subset which is bounded above has a least upper bound.

Defined in
Mathlib.Order.ConditionallyCompleteLattice.Defs
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
ConditionallyCompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isLUB_csSup · cited by 34isLUB_csSupconditionallyCompleteLatticeOfLatticeOfsInf · cited by 0conditionallyCompleteLatt…conditionallyCompleteLatticeOfLatticeOfsSup · cited by 0conditionallyCompleteLatt…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySupSet.sSup · cited by 954SupSet.sSupBddAbove · cited by 620BddAboveConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…IsLUB · cited by 280IsLUBConditionallyCompleteLattice.…CITED BYCITES

Cites6

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Cited by3

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