Theorems · Theorem · logic and foundations
Cardinal.extend_function
∀ {α : Type u_1} {β : Type u_2} {s : Set α} (f : ↑s ↪ β),
Nonempty (↑sᶜ ≃ ↑(Set.range ⇑f)ᶜ) → ∃ g, ∀ (x : ↑s), g ↑x = f x- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement and proof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Equiv.symmproof · cited by 3,681
- Compl.complstatement and proof · cited by 2,925
- Function.Embeddingstatement and proof · cited by 988
- Equiv.transproof · cited by 337
- Equiv.ofInjectiveproof · cited by 64
- Function.Embedding.inj'proof · cited by 29
- Equiv.sumCongrproof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.extend_function_finiteproof · cited by 1
- Cardinal.extend_function_of_ltproof · cited by 0