Theorems · Theorem · general topology
BddAbove.isBounded_inter
∀ {α : Type u_1} {s t : Set α} [inst : Bornology α] [inst_1 : Preorder α] [IsOrderBornology α],
BddAbove s → BddBelow t → Bornology.IsBounded (s ∩ t)- Defined in
- Mathlib.Topology.Order.Bornology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- BddAbovestatement and proof · cited by 620
- BddBelowstatement and proof · cited by 401
- Set.inter_subset_leftproof · cited by 360
- Set.inter_subset_rightproof · cited by 329
- Bornology.IsBoundedstatement · cited by 293
- Bornologystatement and proof · cited by 188
- BddAbove.monoproof · cited by 27
- IsOrderBornologystatement and proof · cited by 20
- BddBelow.monoproof · cited by 16
- BddAbove.isBoundedproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.lowerClosure_piproof · cited by 2