Theorems · Theorem · logic and foundations
exists_surjective_nat
∀ (α : Sort u) [Nonempty α] [Countable α], ∃ f, Function.Surjective f
- Defined in
- Mathlib.Data.Countable.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, 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.
- Countablestatement and proof · cited by 633
- Function.invFunproof · cited by 60
- Function.invFun_surjectiveproof · cited by 8
- Countable.exists_injective_natproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- MeasurableSet.iUnionproof · cited by 81
- countable_iff_exists_surjectiveproof · cited by 3
- Measurable.liminf'proof · cited by 2
- Filter.HasBasis.liminf_eq_ciSup_ciInfproof · cited by 2
- MeasureTheory.StronglyMeasurable.of_discreteproof · cited by 2
- CategoryTheory.Limits.IsFiltered.sequentialFunctor_final_auxproof · cited by 0
- MeasureTheory.Measure.sigmaFinite_iff_measure_singleton_lt_topproof · cited by 0
- CategoryTheory.Limits.IsFiltered.sequentialFunctor_mapproof · cited by 0
- CategoryTheory.Limits.IsCofiltered.sequentialFunctor_initial_auxproof · cited by 0
- CategoryTheory.Limits.IsCofiltered.sequentialFunctor_mapproof · cited by 0