Theorems · Theorem · order theory
sup_iSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] [Nonempty ι] {f : ι → α} {a : α}, a ⊔ ⨆ x, f x = ⨆ x, a ⊔ f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLatticeNonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_constproof · cited by 13
- iSup_sup_eqproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Set.union_iUnionproof · cited by 4
- Language.add_iSupproof · cited by 0