Theorems · Theorem · combinatorics
Finset.le_card_of_inj_on_range
∀ {α : Type u_1} {s : Finset α} {n : ℕ} (f : ℕ → α),
(∀ i < n, f i ∈ s) → (∀ i < n, ∀ j < n, f i = f j → i = j) → n ≤ s.cardSee also Finset.card_le_card_of_injOn, which is a more general version of this lemma.
TODO: consider deprecating, since this is just a special case of Finset.card_le_card_of_injOn.
- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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.
- Finsetstatement and proof · cited by 13,712
- Finset.cardstatement · cited by 2,327
- Set.InjOnproof · cited by 543
- Finset.card_rangeproof · cited by 108
- Finset.coe_rangeproof · cited by 33
- Finset.card_le_card_of_injOnproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- orderOf_le_card_univproof · cited by 3
- addOrderOf_le_card_univproof · cited by 1
- Set.le_ncard_of_inj_on_rangeproof · cited by 0