Theorems · Theorem · order theory
Set.Infinite.exists_ne_map_eq_of_mapsTo
∀ {α : Type u} {β : Type v} {s : Set α} {t : Set β} {f : α → β},
s.Infinite → Set.MapsTo f s t → t.Finite → ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ f x = f y- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Finitestatement and proof · cited by 1,814
- Set.MapsTostatement and proof · cited by 732
- Set.Infinitestatement and proof · cited by 263
- not_imp_notproof · cited by 63
- Set.infinite_of_injOn_mapsToproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- ZLattice.rankproof · cited by 5
- Pell.exists_of_not_isSquareproof · cited by 3
- Set.Infinite.exists_lt_map_eq_of_mapsToproof · cited by 2
- NumberField.Embeddings.pow_eq_one_of_norm_le_oneproof · cited by 2