Theorems · Theorem · order theory
Set.Finite.exists_ge
∀ {α : Type u_2} [Nonempty α] [inst : Preorder α] [IsCodirectedOrder α] {s : Set α}, s.Finite → ∃ M, ∀ i ∈ s, M ≤ i- Defined in
- Mathlib.Data.Fintype.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Finitestatement and proof · cited by 1,814
- IsCodirectedOrderstatement and proof · cited by 95
- directed_idproof · cited by 7
- Directed.finite_set_leproof · cited by 3
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