Theorems · Theorem · order theory
Set.singleton_eq_singleton_iff
∀ {α : Type u_1} {x y : α}, {x} = {y} ↔ x = y- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ext_iffproof · cited by 90
- eq_iff_eq_cancel_leftproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- Set.image_injectiveproof · cited by 15
- Cardinal.cantorproof · cited by 12
- Set.singleton_injectiveproof · cited by 9
- Continuous.image_eq_of_connectedComponent_eqproof · cited by 2
- AddSubmonoid.bot_prod_botproof · cited by 1
- AddSubgroup.bot_prod_botproof · cited by 1
- AddAction.IsBlock.singletonproof · cited by 1
- Topology.RelCWComplex.openCell_zero_injectiveproof · cited by 1
- Topology.RelCWComplex.closedCell_zero_injectiveproof · cited by 1
- PrimeSpectrum.residueField_comapproof · cited by 0
- AddAction.stabilizer_singletonproof · cited by 0
- Semiquot.pure_injproof · cited by 0