Theorems · Theorem · order theory
upperBounds_iUnion
∀ {α : Type u_1} [inst : Preorder α] {ι : Sort u_2} {s : ι → Set α}, upperBounds (⋃ i, s i) = ⋂ i, upperBounds (s i)- Defined in
- Mathlib.Order.Bounds.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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
- Preorderstatement and proof · cited by 7,952
- Set.iUnionstatement · cited by 2,483
- Set.iInterstatement · cited by 1,084
- upperBoundsstatement · cited by 263
- GaloisConnection.l_iSupproof · cited by 78
- gc_upperBounds_lowerBoundsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isLUB_iUnion_iff_of_isLUBproof · cited by 1