Theorems · Theorem · order theory
Finset.inf_mem_of_nonempty
∀ {α : Type u_2} {ι : Type u_5} [inst : LinearOrder α] [inst_1 : OrderTop α] {s : Finset ι} {f : ι → α},
s.Nonempty → s.inf f ∈ f '' ↑s- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderOrderTop
Around this declaration
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Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Finset.Nonemptystatement and proof · cited by 1,001
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- Set.mem_image_of_memproof · cited by 371
- le_totalproof · cited by 294
- Finset.infstatement and proof · cited by 219
- Set.image_monoproof · cited by 197
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