Theorems · Theorem · order theory
iSup_univ
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α}, ⨆ x ∈ Set.univ, f x = ⨆ x, f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement · cited by 3,945
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_congr_Propproof · cited by 247
- iSup_posproof · cited by 61
Cited by8
Results whose statement or proof uses this declaration.
- Set.biUnion_univproof · cited by 11
- sup_iSup_nat_succproof · cited by 3
- iInf_iSup_of_monotoneproof · cited by 3
- Set.map_finite_iSupproof · cited by 1
- IsSemisimpleModule.supproof · cited by 0
- ExpGrowth.expGrowthSup_iSupproof · cited by 0
- LinearGrowth.linearGrowthSup_iSupproof · cited by 0
- Filter.iSup_pure_eq_topproof · cited by 0