Theorems · Theorem · order theory
csSup_union
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s t : Set α},
BddAbove s → s.Nonempty → BddAbove t → t.Nonempty → sSup (s ∪ t) = sSup s ⊔ sSup tThe sSup of a union of two sets is the max of the suprema of each subset, under the
assumptions that all sets are bounded above and nonempty.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- isLUB_csSupproof · cited by 34
- IsLUB.csSup_eqproof · cited by 19
- IsLUB.unionproof · cited by 5
- Set.Nonempty.inlproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.