Mathlib Map

Theorems · Theorem · order theory

Set.notMem_singleton_empty

∀ {α : Type u_1} {s : Set α}, s ∉ {∅} ↔ s.Nonempty
Defined in
Mathlib.Data.Set.Insert
Cited by
2 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Partition.nonempty_of_mem · cited by 3Partition.nonempty_of_memSet.Countable.dense_compl · cited by 1Countable.dense_complSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.nonempty_iff_ne_empty · cited by 96Set.nonempty_iff_ne_emptySet.notMem_singleton_emptyCITED BYCITES

Cites3

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

Cited by2

Results whose statement or proof uses this declaration.