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Theorems · Theorem · order theory

csInf_singleton

∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderInf α] (a : α), sInf {a} = a
Defined in
Mathlib.Order.ConditionallyCompletePartialOrder.Basic
Cited by
6 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
ConditionallyCompletePartialOrderInf
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Around this declaration

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

ciInf_const · cited by 20ciInf_constReal.sInf_smul_of_nonneg · cited by 3Real.sInf_smul_of_nonnegReal.sInf_smul_of_nonpos · cited by 1Real.sInf_smul_of_nonposcsInf_zero · cited by 0csInf_zeroMeasureTheory.hittingBtwn_of_le · cited by 0MeasureTheory.hittingBtwn…csInf_one · cited by 0csInf_oneSet · cited by 53352SetInfSet.sInf · cited by 935InfSet.sInfConditionallyCompletePartialOrderInf · cited by 51ConditionallyCompletePart…IsLeast.csInf_eq · cited by 11IsLeast.csInf_eqisLeast_singleton · cited by 5isLeast_singletoncsInf_singletonCITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.