Theorems · Theorem · order theory
IsGreatest.csSup_eq
∀ {α : Type u_1} [inst : ConditionallyCompletePartialOrderSup α] {s : Set α} {a : α}, IsGreatest s a → sSup s = aA greatest element of a set is the supremum of this set.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
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
- SupSet.sSupstatement · cited by 954
- IsGreateststatement and proof · cited by 112
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- IsGreatest.isLUBproof · cited by 25
- IsLUB.uniqueproof · cited by 21
- DirectedOn.isLUB_csSupproof · cited by 9
- IsGreatest.nonemptyproof · cited by 2
- IsGreatest.directedOnproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- csSup_singletonproof · cited by 6
- csSup_Iicproof · cited by 5
- csSup_Iccproof · cited by 3
- MonotoneOn.exists_monotone_extensionproof · cited by 2
- CStarModule.norm_eq_csSupproof · cited by 0
- IsGreatest.csSup_memproof · cited by 0
- Polynomial.supNorm_eq_iSupproof · cited by 0
- csSup_Iocproof · cited by 0
- sup_eq_top_of_top_memproof · cited by 0