Theorems · Theorem · order theory
Set.bounded_ge_inter_not_ge
∀ {α : Type u_1} {s : Set α} [inst : SemilatticeInf α] (a : α),
Set.Bounded (fun x1 x2 => x1 ≥ x2) (s ∩ {b | ¬a ≤ b}) ↔ Set.Bounded (fun x1 x2 => x1 ≥ x2) s- Defined in
- Mathlib.Order.Bounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
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Cites5
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
- Set.ofPredstatement · cited by 6,101
- SemilatticeInfstatement and proof · cited by 634
- Set.Boundedstatement · cited by 57
- Set.bounded_le_inter_not_leproof · cited by 2
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