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Theorems · Theorem · order theory

csSup_Icc

∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderSup α] {a b : α}, a ≤ b → sSup (Set.Icc a b) = b
Defined in
Mathlib.Order.ConditionallyCompletePartialOrder.Basic
Cited by
3 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
ConditionallyCompletePartialOrderSup
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Around this declaration

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

Real.ediam_Icc · cited by 5Real.ediam_IccRootPairing.coe_chainBotCoeff_eq_sSup · cited by 1RootPairing.coe_chainBotC…RootPairing.coe_chainTopCoeff_eq_sSup · cited by 0RootPairing.coe_chainTopC…Set.Icc · cited by 1702Set.IccSupSet.sSup · cited by 954SupSet.sSupConditionallyCompletePartialOrderSup · cited by 52ConditionallyCompletePart…IsGreatest.csSup_eq · cited by 9IsGreatest.csSup_eqisGreatest_Icc · cited by 4isGreatest_IcccsSup_IccCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.