Theorems · Theorem · order theory
cbiSup_eq_of_forall
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderSup α] {p : ι → Prop} {f : Subtype p → α},
(∀ (i : ι), p i) → ⨆ i, ⨆ (h : p i), f ⟨i, h⟩ = iSup f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- SupSet.sSupproof · cited by 954
- iSup_congr_Propproof · cited by 247
- Set.Subset.antisymmproof · cited by 213
- SupSetproof · cited by 154
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- ciSup_uniqueproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Measurable.biSupproof · cited by 3
- IsNonarchimedean.apply_sum_univ_leproof · cited by 1