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Theorems · Theorem · order theory

Set.Nonempty.csInf_mem

∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] {s : Set α}, s.Nonempty → s.Finite → sInf s ∈ s
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Finset
Cited by
3 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLinearOrder
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Around this declaration

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

Set.Nonempty.ordConnected_iff_of_bdd · cited by 3Nonempty.ordConnected_iff…exists_eq_ciInf_of_finite · cited by 0exists_eq_ciInf_of_finiteSet.Finite.map_sInf_of_monotone · cited by 0Finite.map_sInf_of_monoto…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.Finite · cited by 1814Set.FiniteInfSet.sInf · cited by 935InfSet.sInfConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…Set.Nonempty.csSup_mem · cited by 11Nonempty.csSup_memNonempty.csInf_memCITED BYCITES

Cites6

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.