Theorems · Theorem · order theory
Set.bounded_lt_inter_not_lt
∀ {α : Type u_1} {s : Set α} [inst : SemilatticeSup α] (a : α),
Set.Bounded (fun x1 x2 => x1 < x2) (s ∩ {b | ¬b < a}) ↔ Set.Bounded (fun x1 x2 => x1 < x2) s- Defined in
- Mathlib.Order.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SemilatticeSupstatement and proof · cited by 785
- Set.Boundedstatement · cited by 57
- Set.bounded_inter_notproof · cited by 3
- lt_sup_of_lt_rightproof · cited by 1
- lt_sup_of_lt_leftproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Set.unbounded_lt_inter_not_ltproof · cited by 2
- Set.bounded_lt_inter_leproof · cited by 1
- Set.bounded_gt_inter_not_gtproof · cited by 0