Theorems · Theorem · logic and foundations
Function.exists_surjective_iff
∀ {α : Sort u_1} {β : Sort u_2}, (∃ f, Function.Surjective f) ↔ Nonempty (α → β) ∧ Nonempty (β ↪ α)- Defined in
- Mathlib.Logic.Embedding.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Function.Embeddingstatement and proof · cited by 988
- IsEmptyproof · cited by 759
- Function.surjInvproof · cited by 63
- Function.invFunproof · cited by 60
- isEmptyElimproof · cited by 59
- Function.Embedding.inj'proof · cited by 29
- Function.Embedding.toFunproof · cited by 25
- Function.injective_surjInvproof · cited by 14
- Function.invFun_surjectiveproof · cited by 8
- nonempty_funproof · cited by 1
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