Theorems · Theorem · combinatorics
Finset.card_le_card_of_injOn
∀ {α : Type u_1} {β : Type u_2} {s : Finset α} {t : Finset β} (f : α → β),
Set.MapsTo f ↑s ↑t → Set.InjOn f ↑s → s.card ≤ t.card- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SetLike.coestatement and proof · cited by 8,199
- Finset.cardstatement · cited by 2,327
- Set.MapsTostatement and proof · cited by 732
- Set.InjOnstatement and proof · cited by 543
- Finset.card_le_cardproof · cited by 118
- Finset.card_image_of_injOnproof · cited by 36
- Finset.image_subset_iffproof · cited by 12
Cited by16
Results whose statement or proof uses this declaration.
- Fintype.card_le_of_injectiveproof · cited by 19
- Finset.exists_ne_map_eq_of_card_lt_of_maps_toproof · cited by 5
- Finset.card_le_card_image₂_leftproof · cited by 4
- Finset.card_le_card_image₂_rightproof · cited by 4
- Finset.le_card_of_inj_on_rangeproof · cited by 3
- Finset.ruzsa_triangle_inequality_div_div_divproof · cited by 3
- Finset.ruzsa_triangle_inequality_sub_sub_subproof · cited by 3
- Finset.le_mulEnergyproof · cited by 2
- Finset.le_addEnergyproof · cited by 2
- Dynamics.IsDynNetIn.card_le_card_of_isDynCoverOfproof · cited by 1
- card_nthRoots_subgroup_unitsproof · cited by 1
- BoxIntegral.Prepartition.card_filter_mem_Icc_leproof · cited by 1