Theorems · Theorem · order theory
isLUB_biSup
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {s : Set β} {f : β → α}, IsLUB (f '' s) (⨆ x ∈ s, f x)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Elemproof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- IsLUBstatement and proof · cited by 280
- Set.range_compproof · cited by 223
- Subtype.range_coeproof · cited by 98
- iSup_subtype'proof · cited by 44
- isLUB_iSupproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Sion.minimax'proof · cited by 1