Theorems · Theorem · order theory
exists_sSupIndep_of_sSup_atoms_eq_top
∀ {α : Type u_2} [inst : CompleteLattice α] [IsModularLattice α] [IsCompactlyGenerated α],
sSup {a | IsAtom a} = ⊤ → ∃ s, sSupIndep s ∧ sSup s = ⊤ ∧ ∀ ⦃a : α⦄, a ∈ s → IsAtom a- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.ofPredstatement and proof · cited by 6,101
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- IsAtomstatement and proof · cited by 130
- IsModularLatticestatement and proof · cited by 86
- sSupIndepstatement · cited by 39
- IsCompactlyGeneratedstatement and proof · cited by 37
- exists_sSupIndep_of_sSup_atomsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsSemisimpleModule.exists_sSupIndep_sSup_simples_eq_topproof · cited by 2