Theorems · Definition · order theory
sSupIndep
{α : Type u_1} → [CompleteLattice α] → Set α → PropAn independent set of elements in a complete lattice is one in which every element is disjoint
from the Sup of the rest.
- Defined in
- Mathlib.Order.SupIndep
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Disjointproof · cited by 2,201
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
Cited by47
Results whose statement or proof uses this declaration.
- Partition.removeBotstatement and proof · cited by 4
- sSupIndep.monostatement and proof · cited by 4
- sSupIndep.pairwiseDisjointstatement and proof · cited by 4
- IsSemisimpleModule.exists_linearEquiv_dfinsuppstatement and proof · cited by 3
- sSupIndep_iffstatement · cited by 3
- sSupIndep_singletonstatement · cited by 3
- complementedLattice_of_sSup_atoms_eq_topproof · cited by 3
- WellFoundedGT.finite_of_sSupIndepstatement and proof · cited by 2
- iSupIndep.sSupIndep_rangestatement · cited by 2
- IsSemisimpleModule.exists_sSupIndep_sSup_simples_eq_topstatement and proof · cited by 2
- exists_sSupIndep_disjoint_sSup_atomsstatement and proof · cited by 2
- IsSemisimpleModule.finite_tfaestatement and proof · cited by 2