Theorems · Theorem · order theory
lowerBounds_union
∀ {α : Type u_1} [inst : Preorder α] {s t : Set α}, lowerBounds (s ∪ t) = lowerBounds s ∩ lowerBounds t- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.Subset.antisymmproof · cited by 213
- lowerBoundsstatement and proof · cited by 212
Cited by3
Results whose statement or proof uses this declaration.
- lowerBounds_insertproof · cited by 3
- BddBelow.unionproof · cited by 1
- isLeast_union_iffproof · cited by 0