Theorems · Theorem · order theory
Set.Subsingleton.induction_on
∀ {α : Type u} {s : Set α} {p : Set α → Prop}, s.Subsingleton → p ∅ → (∀ (x : α), p {x}) → p s- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, 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 and proof · cited by 53,352
- Set.Subsingletonstatement and proof · cited by 276
- Set.Subsingleton.eq_empty_or_singletonproof · cited by 16
Cited by12
Results whose statement or proof uses this declaration.
- Set.Subsingleton.finiteproof · cited by 20
- Set.Subsingleton.measurableSetproof · cited by 3
- Set.Subsingleton.measure_zeroproof · cited by 3
- Set.Subsingleton.isCompactproof · cited by 2
- MulAction.IsBlock.of_subsingletonproof · cited by 1
- AddAction.IsBlock.of_subsingletonproof · cited by 1
- Filter.biInter_mem'proof · cited by 1
- Set.Subsingleton.holderOnWithproof · cited by 0
- Set.Subsingleton.isPreconnectedproof · cited by 0
- Set.Subsingleton.isLindelofproof · cited by 0
- Set.Subsingleton.continuousOnproof · cited by 0
- Set.Subsingleton.differentiableOnproof · cited by 0