Theorems · Theorem · combinatorics
Finite.exists_infinite_fiber
∀ {α : Type u_1} {β : Type u_2} [Infinite α] [Finite β] (f : α → β), ∃ y, Infinite ↑(f ⁻¹' {y})The strong pigeonhole principle for infinitely many pigeons in
finitely many pigeonholes. If there are infinitely many pigeons in
finitely many pigeonholes, then there is a pigeonhole with infinitely
many pigeons.
See also: Finite.exists_ne_map_eq_of_infinite
- Defined in
- Mathlib.Data.Fintype.Pigeonhole
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.preimagestatement and proof · cited by 4,946
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- Infinitestatement and proof · cited by 352
- nonempty_fintypeproof · cited by 261
- Finset.biUnionproof · cited by 217
- Set.toFinsetproof · cited by 217
- Fintype.falseproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- exists_seq_forall_proj_of_forall_finiteproof · cited by 0