Theorems · Theorem · order theory
LowerSet.compl_iSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : LE α] (f : ι → LowerSet α), (⨆ i, f i).compl = ⨆ i, (f i).compl- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Compl.complproof · cited by 2,925
- iSupstatement · cited by 2,415
- Set.iInterproof · cited by 1,084
- UpperSetstatement · cited by 245
- LowerSetstatement and proof · cited by 230
- Set.compl_iUnionproof · cited by 32
- UpperSet.extproof · cited by 29
- LowerSet.complstatement and proof · cited by 17
- LowerSet.coe_iSupproof · cited by 5
- UpperSet.coe_iSupproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- LowerSet.compl_iSup₂proof · cited by 0