Theorems · Theorem · order theory
ciSup_prod
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : ConditionallyCompleteLattice α] {f : β × γ → α},
BddAbove (Set.range f) → ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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.
Cites15
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 and proof · cited by 2,415
- 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
- Set.mem_rangeproof · cited by 102
- eq_of_forall_ge_iffproof · cited by 96
- ciSup_leproof · cited by 56
- ciSup_constproof · cited by 43
- iSup_of_empty'proof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Finite.ciSup_prodproof · cited by 2
- ciInf_prodproof · cited by 0