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Theorems · Theorem · order theory

Finset.Nonempty.csSup_mem

∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] {s : Finset α}, s.Nonempty → sSup ↑s ∈ s
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Finset
Cited by
2 results in Mathlib
Foundations
Depth 73 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.csSup_mem · cited by 11Nonempty.csSup_memFinset.Nonempty.csInf_mem · cited by 0Nonempty.csInf_memFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeFinset.Nonempty · cited by 1001Finset.NonemptySupSet.sSup · cited by 954SupSet.sSupConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…Finset.max'_mem · cited by 30Finset.max'_memFinset.Nonempty.csSup_eq_max' · cited by 5Nonempty.csSup_eq_max'Nonempty.csSup_memCITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.