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Theorems · Theorem · group theory

Set.isUnit_iff_singleton

∀ {α : Type u_2} [inst : Group α] {s : Set α}, IsUnit s ↔ ∃ a, s = {a}
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
0 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Group
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Around this declaration

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

Set · cited by 53352SetGroup · cited by 6238GroupIsUnit · cited by 1602IsUnitSet.monoid · cited by 19Set.monoidSet.isUnit_iff_singletonCITED BYCITES

Cites4

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

  • Setstatement and proof · cited by 53,352
  • Groupstatement and proof · cited by 6,238
  • IsUnitstatement · cited by 1,602
  • Set.monoidstatement · cited by 19

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.