Theorems · Theorem · order theory
Set.Infinite.exists_lt_map_eq_of_mapsTo
∀ {α : Type u_2} {β : Type u_3} [inst : LinearOrder α] {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.Order.Preorder.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Finitestatement and proof · cited by 1,814
- Set.MapsTostatement and proof · cited by 732
- Set.Infinitestatement and proof · cited by 263
- Ne.lt_or_gtproof · cited by 108
- Set.Infinite.exists_ne_map_eq_of_mapsToproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Set.Finite.exists_lt_map_eq_of_forall_memproof · cited by 6
- Nat.exists_lt_modEq_of_infiniteproof · cited by 1