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Theorems · Theorem · order theory

csSup_Ioo

∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {a b : α} [DenselyOrdered α], a < b → sSup (Set.Ioo a b) = b
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLatticeDenselyOrdered
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Around this declaration

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

Real.ediam_Ioo · cited by 3Real.ediam_IooSet.Ioo · cited by 1214Set.IooSupSet.sSup · cited by 954SupSet.sSupDenselyOrdered · cited by 471DenselyOrderedConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…Set.nonempty_Ioo · cited by 23Set.nonempty_IooIsLUB.csSup_eq · cited by 19IsLUB.csSup_eqisLUB_Ioo · cited by 7isLUB_IoocsSup_IooCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.