Theorems · Theorem · order theory
complementedLattice_of_complementedLattice_Iic
∀ {ι : Type u_1} {α : Type u_2} [inst : CompleteLattice α] [IsModularLattice α] [IsCompactlyGenerated α] {s : Set ι}
{f : ι → α}, (∀ i ∈ s, ComplementedLattice ↑(Set.Iic (f i))) → ⨆ i ∈ s, f i = ⊤ → ComplementedLattice α- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.rangeproof · cited by 4,705
- Set.iUnionproof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- Set.Iicstatement and proof · cited by 1,111
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- eq_top_iffproof · cited by 236
Cited by1
Results whose statement or proof uses this declaration.
- isSemisimpleModule_of_isSemisimpleModule_submoduleproof · cited by 2