Theorems · Theorem · order theory
Finset.supIndep_iff_pairwiseDisjoint
∀ {α : Type u_1} {ι : Type u_3} [inst : DistribLattice α] [inst_1 : OrderBot α] {s : Finset ι} {f : ι → α},
s.SupIndep f ↔ (↑s).PairwiseDisjoint f- Defined in
- Mathlib.Order.SupIndep
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DistribLatticeOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- OrderBotstatement and proof · cited by 1,055
- Set.PairwiseDisjointstatement and proof · cited by 275
- DistribLatticestatement and proof · cited by 150
- Finset.SupIndepstatement · cited by 52
- Finset.SupIndep.pairwiseDisjointproof · cited by 7
- Finset.disjoint_sup_rightproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.IsSetSemiring.exists_finpartition_sdiffproof · cited by 8
- Set.PairwiseDisjoint.supIndepproof · cited by 1
- MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_memproof · cited by 1