Theorems · Theorem · order theory
isLUB_iSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α}, IsLUB (Set.range f) (⨆ j, f j)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 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 · cited by 280
- isLUB_sSupproof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- iSup_le_iffproof · cited by 45
- CountableSupClosed.iSup_memproof · cited by 3
- CountableSupClosed.of_iSup_memproof · cited by 1
- isLUB_biSupproof · cited by 1
- Function.sSup_div_semiconjproof · cited by 0
- iUnion_Iio_eq_Iio_iSupproof · cited by 0