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Theorems · Theorem · order theory

Setoid.empty_notMem_classes

∀ {α : Type u_1} {r : Setoid α}, ∅ ∉ r.classes

The empty set is not an equivalence class.

Defined in
Mathlib.Data.Setoid.Partition
Cited by
1 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
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Around this declaration

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

Setoid.isPartition_classes · cited by 1Setoid.isPartition_classesSet · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredSet.notMem_empty · cited by 35Set.notMem_emptySetoid.classes · cited by 17Setoid.classesSetoid.refl' · cited by 14Setoid.refl'Setoid.empty_notMem_classesCITED BYCITES

Cites5

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

Cited by1

Results whose statement or proof uses this declaration.