Theorems · Theorem · order theory
csSup_insert
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α},
BddAbove s → s.Nonempty → sSup (insert a s) = a ⊔ sSup sThe supremum of insert a s is the maximum of a and the supremum of s, if s is
nonempty and bounded above.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
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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
- Set.insert_nonemptyproof · cited by 13
- IsLUB.insertproof · cited by 4
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