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Theorems · Theorem · order theory

sSupIndep.pairwiseDisjoint

∀ {α : Type u_1} [inst : CompleteLattice α] {s : Set α}, sSupIndep s → s.PairwiseDisjoint id

If the elements of a set are independent, then any pair within that set is disjoint.

Defined in
Mathlib.Order.SupIndep
Cited by
4 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
CompleteLattice
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Partition.pairwiseDisjoint · cited by 1Partition.pairwiseDisjointPartition.disjoint · cited by 1Partition.disjointsSupIndep_iff_pairwiseDisjoint · cited by 1sSupIndep_iff_pairwiseDis…sSupIndep_pair · cited by 0sSupIndep_pairSet · cited by 53352SetCompleteLattice · cited by 1048CompleteLatticeSet.PairwiseDisjoint · cited by 275Set.PairwiseDisjointsSupIndep · cited by 39sSupIndepSet.mem_sdiff · cited by 31Set.mem_sdiffdisjoint_sSup_right · cited by 2disjoint_sSup_rightsSupIndep.pairwiseDisjointCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.