Theorems · Theorem · combinatorics
Finite.of_surjective
∀ {α : Sort u_4} {β : Sort u_5} [Finite α] (f : α → β), Function.Surjective f → Finite β- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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.
- Finitestatement and proof · cited by 3,029
- Function.surjInvproof · cited by 63
- Finite.of_injectiveproof · cited by 32
- Function.injective_surjInvproof · cited by 14
Cited by14
Results whose statement or proof uses this declaration.
- Module.finite_of_finiteproof · cited by 8
- Equiv.Perm.exists_extending_pairproof · cited by 2
- Sylow.mapSurjective_surjectiveproof · cited by 2
- Infinite.of_surjectiveproof · cited by 2
- SSet.finite_of_hasDimensionLTproof · cited by 2
- Ideal.IsFractionRing.finite_of_isInvariantproof · cited by 2
- Profinite.exists_lift_of_finite_of_injective_of_surjectiveproof · cited by 1
- SSet.finite_iSup_iffproof · cited by 1
- Finite.prod_leftproof · cited by 1
- Finite.prod_rightproof · cited by 1
- IsLocalRing.finite_quotient_iffproof · cited by 0
- SSet.finite_of_epiproof · cited by 0