Theorems · Theorem · order theory
IsLUB.iSup_eq
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α} {a : α}, IsLUB (Set.range f) a → ⨆ j, f j = a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- IsLUBstatement and proof · cited by 280
- IsLUB.sSup_eqproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- GaloisConnection.l_iSupproof · cited by 78