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Theorems · Theorem · order theory

csSup_Iic

∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderSup α] {a : α}, sSup (Set.Iic a) = a
Defined in
Mathlib.Order.ConditionallyCompletePartialOrder.Basic
Cited by
5 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
ConditionallyCompletePartialOrderSup
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Around this declaration

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

Ordinal.iSup_typein_succ · cited by 2Ordinal.iSup_typein_succOrder.IsNormal.preimage_Iic · cited by 2IsNormal.preimage_IicPointedCone.lineal_eq_sSup · cited by 0PointedCone.lineal_eq_sSupRootPairing.chainTopCoeff_eq_sSup · cited by 0RootPairing.chainTopCoeff…RootPairing.chainBotCoeff_eq_sSup · cited by 0RootPairing.chainBotCoeff…Set.Iic · cited by 1111Set.IicSupSet.sSup · cited by 954SupSet.sSupConditionallyCompletePartialOrderSup · cited by 52ConditionallyCompletePart…IsGreatest.csSup_eq · cited by 9IsGreatest.csSup_eqisGreatest_Iic · cited by 4isGreatest_IiccsSup_IicCITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.