Theorems · Theorem · combinatorics
Function.Embedding.nonempty_of_card_le
∀ {α : Type u_1} {β : Type u_2} [inst : Fintype α] [inst_1 : Fintype β],
Fintype.card α ≤ Fintype.card β → Nonempty (α ↪ β)- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement and proof · cited by 1,386
- Function.Embeddingstatement · cited by 988
- Trunc.nonemptyproof · cited by 2
- Function.Embedding.truncOfCardLEproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- SimpleGraph.recolorOfCardLEproof · cited by 4
- Function.Embedding.exists_of_card_le_finsetproof · cited by 2
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2
- Function.Embedding.nonempty_iff_card_leproof · cited by 2
- Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_cardproof · cited by 2
- SimpleGraph.bot_isContained_iff_card_leproof · cited by 1
- SimpleGraph.coe_recolorOfCardLEstatement · cited by 0