Theorems · Theorem · order theory
IsLUB.csSup_eq
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α}, IsLUB s a → s.Nonempty → sSup s = a- Cited by
- 19 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
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
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement · cited by 954
- ConditionallyCompleteLatticestatement and proof · cited by 364
- IsLUBstatement and proof · cited by 280
- isLUB_csSupproof · cited by 34
- IsLUB.uniqueproof · cited by 21
Cited by19
Results whose statement or proof uses this declaration.
- Order.IsNormal.map_sSupproof · cited by 5
- csSup_image2_eq_csSup_csSupproof · cited by 5
- Order.IsSuccPrelimit.sSup_Iioproof · cited by 4
- MonotoneOn.map_csSup_of_continuousWithinAtproof · cited by 4
- ConvexOn.sSup_of_countable_affine_eqproof · cited by 2
- IsLUB.mem_of_nonempty_of_not_isSuccLimitproof · cited by 2
- LeftOrdContinuous.map_csSupproof · cited by 2
- IsLUB.ciSup_eqproof · cited by 1
- IsLUB.ciSup_set_eqproof · cited by 1
- MonotoneOn.sSup_image_Iccproof · cited by 1
- ConvexOn.univ_sSup_of_countable_affine_eqproof · cited by 1
- csSup_Iooproof · cited by 1