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Theorems · Theorem · order theory

Set.bounded_le_iff_bounded_lt

∀ {α : Type u_1} {s : Set α} [inst : Preorder α] [NoMaxOrder α],
  Set.Bounded (fun x1 x2 => x1 ≤ x2) s ↔ Set.Bounded (fun x1 x2 => x1 < x2) s
Defined in
Mathlib.Order.Bounded
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
PreorderNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.bounded_lt_inter_lt · cited by 2Set.bounded_lt_inter_ltSet.bounded_ge_iff_bounded_gt · cited by 0Set.bounded_ge_iff_bounde…Set · cited by 53352SetPreorder · cited by 7952Preorderlt_of_le_of_lt · cited by 432lt_of_le_of_ltNoMaxOrder · cited by 340NoMaxOrderNoMaxOrder.exists_gt · cited by 62NoMaxOrder.exists_gtSet.Bounded · cited by 57Set.BoundedSet.bounded_le_of_bounded_lt · cited by 2Set.bounded_le_of_bounded…Set.bounded_le_iff_bounded_ltCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.