Theorems · Theorem · combinatorics
Fintype.card_lt_of_injective_of_notMem
∀ {α : Type u_1} {β : Type u_2} [inst : Fintype α] [inst_1 : Fintype β] (f : α → β),
Function.Injective f → ∀ {b : β}, b ∉ Set.range f → Fintype.card α < Fintype.card β- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- Finset.univproof · cited by 3,473
- Fintype.cardstatement · cited by 1,386
- Set.image_univproof · cited by 322
- Finset.coe_mapproof · cited by 114
- Finset.card_mapproof · cited by 114
- Finset.coe_univproof · cited by 101
- Finset.mem_coeproof · cited by 91
Cited by4
Results whose statement or proof uses this declaration.
- Fintype.card_lt_of_injective_not_surjectiveproof · cited by 2
- card_units_ltproof · cited by 2
- Fintype.card_subtype_ltproof · cited by 2
- Fin.lt_of_injective_of_notMemproof · cited by 0