Theorems · Theorem · order theory
LowerSet.coe_iSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : LE α] (f : ι → LowerSet α), ↑(⨆ i, f i) = ⋃ i, ↑(f i)- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LE
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.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.iUnionstatement and proof · cited by 2,483
- iSupstatement · cited by 2,415
- Set.iUnion_congr_Propproof · cited by 374
- LowerSetstatement and proof · cited by 230
- Set.mem_rangeproof · cited by 102
- Set.iUnion_existsproof · cited by 45
- Set.iUnion_iUnion_eq'proof · cited by 21
Cited by5
Results whose statement or proof uses this declaration.
- LowerSet.coe_iSup₂proof · cited by 3
- UpperSet.compl_iSupproof · cited by 1
- LowerSet.compl_iSupproof · cited by 1
- LowerSet.mem_iSup_iffproof · cited by 1
- LowerSet.iSup_Iicproof · cited by 0