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Theorems · Theorem · order theory

csInf_Ici

∀ {α : Type u_5} [inst : ConditionallyCompletePartialOrderInf α] {a : α}, sInf (Set.Ici a) = a
Defined in
Mathlib.Order.ConditionallyCompletePartialOrder.Basic
Cited by
5 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
ConditionallyCompletePartialOrderInf
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Around this declaration

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

Filter.limsup_const · cited by 12Filter.limsup_constSubmodule.set_smul_eq_iSup · cited by 2Submodule.set_smul_eq_iSupMeasureTheory.eLpNorm_dirac · cited by 1MeasureTheory.eLpNorm_dir…Filter.sInter_lift'_sets · cited by 1Filter.sInter_lift'_setsMeasureTheory.hittingAfter_univ · cited by 0MeasureTheory.hittingAfte…Set.Ici · cited by 1070Set.IciInfSet.sInf · cited by 935InfSet.sInfConditionallyCompletePartialOrderInf · cited by 51ConditionallyCompletePart…IsLeast.csInf_eq · cited by 11IsLeast.csInf_eqisLeast_Ici · cited by 7isLeast_IcicsInf_IciCITED 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.