Theorems · Theorem · order theory
iSup_sup_eq
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f g : ι → α}, ⨆ x, f x ⊔ g x = (⨆ x, f x) ⊔ ⨆ x, g x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- 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.
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- sup_leproof · cited by 159
- sup_le_supproof · cited by 48
- iSup_monoproof · cited by 37
Cited by7
Results whose statement or proof uses this declaration.
- iSup_insertproof · cited by 10
- iSup_unionproof · cited by 8
- Set.iUnion_union_distribproof · cited by 4
- iSup_supproof · cited by 3
- sup_iSupproof · cited by 2
- Filter.sup_limsupproof · cited by 2
- iSup_diteproof · cited by 2