Theorems · Theorem
Function.cantor_injective
∀ {α : Type u_4} (f : Set α → α), ¬Function.Injective fCantor's diagonal argument implies that there are no injective functions from Set α
to α.
- Defined in
- Mathlib.Logic.Function.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Set.ofPredproof · cited by 6,101
- Set.extproof · cited by 2,266
- Function.cantor_surjectiveproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.cantorproof · cited by 12
- Function.not_surjective_Typeproof · cited by 0
- not_small_typeproof · cited by 0