Theorems · Theorem · order theory
BddBelow.inter_of_left
∀ {α : Type u_1} [inst : Preorder α] {s t : Set α}, BddBelow s → BddBelow (s ∩ t)If s is bounded, then so is s ∩ t
- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Preorderstatement and proof · cited by 7,952
- BddBelowstatement and proof · cited by 401
- Set.inter_subset_leftproof · cited by 360
- BddBelow.monoproof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.hittingBtwn_leproof · cited by 8
- MeasureTheory.hittingBtwn_eq_hittingBtwn_of_existsproof · cited by 3
- MeasureTheory.hittingBtwn_le_of_memproof · cited by 2
- MeasureTheory.hittingAfter_le_of_memproof · cited by 2
- IsClosed.exists_wbtw_isVisibleproof · cited by 1
- MeasureTheory.notMem_of_lt_hittingAfterproof · cited by 1
- MeasureTheory.notMem_of_lt_hittingBtwnproof · cited by 0