Theorems · Theorem · order theory
ciSup_sup_eq
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {f g : ι → α},
BddAbove (Set.range f) → BddAbove (Set.range g) → ⨆ x, f x ⊔ g x = (⨆ x, f x) ⊔ ⨆ x, g x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- le_antisymmproof · cited by 2,068
- SupSet.sSupproof · cited by 954
- IsEmptyproof · cited by 759
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- isEmpty_or_nonemptyproof · cited by 269
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_of_le_leftproof · cited by 218
- sup_leproof · cited by 159
Cited by3
Results whose statement or proof uses this declaration.
- ciSup_sup_leproof · cited by 1
- ciInf_inf_eqproof · cited by 0
- Finset.ciSup_unionproof · cited by 0