Theorems · Inductive type · order theory
Partition
{α : Type u_1} → [CompleteLattice α] → α → Type u_1A Partition of an element s of a CompleteLattice is a collection of
independent nontrivial elements whose supremum is s.
- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 91 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteLatticestatement · cited by 1,048
Cited by108
Results whose statement or proof uses this declaration.
- Partition.Relstatement and proof · cited by 22
- Partition.IsRepFunstatement · cited by 17
- Partition.partOfstatement and proof · cited by 13
- Partition.IsRepFun.apply_of_notMemstatement and proof · cited by 7
- Partition.repstatement and proof · cited by 7
- Partition.subset_of_memstatement and proof · cited by 7
- Partition.Rel.symmstatement and proof · cited by 5
- Partition.eq_of_mem_of_memstatement and proof · cited by 5
- Partition.partsstatement and proof · cited by 5
- Partition.IsRepFun.apply_eq_applystatement and proof · cited by 4
- Partition.IsRepFun.rel_applystatement and proof · cited by 4
- Partition.copystatement and proof · cited by 4