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Theorems · Theorem · order theory

Set.exists_lower_bound_image

∀ {α : Type u} {β : Type v} [Nonempty α] [inst : LinearOrder β] (s : Set α) (f : α → β),
  s.Finite → ∃ a, ∀ b ∈ s, f a ≤ f b
Defined in
Mathlib.Data.Set.Finite.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonemptyLinearOrder
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Around this declaration

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

Set.exists_upper_bound_image · cited by 1Set.exists_upper_bound_im…Polynomial.exists_min_root · cited by 0Polynomial.exists_min_rootSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Nonempty · cited by 2627Set.NonemptySet.Finite · cited by 1814Set.FiniteSet.eq_empty_or_nonempty · cited by 248Set.eq_empty_or_nonemptySet.exists_min_image · cited by 4Set.exists_min_imageSet.exists_lower_bound_imageCITED BYCITES

Cites6

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.