Theorems · Theorem · order theory
BddAbove.range_iSup_of_iUnion_range
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {κ : ι → Sort u_5} {f : (i : ι) → κ i → α},
BddAbove (⋃ i, Set.range (f i)) → BddAbove (Set.range fun i => ⨆ j, f i j)If the set of all f i j is bounded above, then so is the set of the supremums of every row
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- Set.iUnionstatement and proof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- SupSet.sSupproof · cited by 954
- IsEmptyproof · cited by 759
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- isEmpty_or_nonemptyproof · cited by 269
- upperBoundsproof · cited by 263
- le_sup_rightproof · cited by 242
- ciSup_leproof · cited by 56
- le_sup_of_le_leftproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- le_ciSup₂proof · cited by 3