Theorems · Theorem · logic and foundations
Nat.card_le_card_of_injective
∀ {α : Type u} {β : Type v} [Finite β] (f : α → β), Function.Injective f → Nat.card α ≤ Nat.card β- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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.
- Finitestatement and proof · cited by 3,029
- Cardinal.mkproof · cited by 942
- Nat.cardstatement · cited by 844
- Cardinal.toNat_liftproof · cited by 41
- Cardinal.toNat_le_toNatproof · cited by 14
- Cardinal.lift_mk_le_lift_mk_of_injectiveproof · cited by 10
Cited by19
Results whose statement or proof uses this declaration.
- Subgroup.exists_pow_mem_of_index_ne_zeroproof · cited by 2
- AddSubgroup.exists_nsmul_mem_of_index_ne_zeroproof · cited by 2
- Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg_of_finiteproof · cited by 2
- SimpleGraph.Colorable.card_le_of_pairwise_adjproof · cited by 2
- SimpleGraph.ncard_oddComponents_monoproof · cited by 1
- Finite.card_le_of_embeddingproof · cited by 1
- Finite.card_le_of_injective'proof · cited by 1
- FiniteField.unitsMap_norm_surjectiveproof · cited by 1
- Subgroup.card_le_card_groupproof · cited by 1
- Function.Injective.bijective_of_nat_card_leproof · cited by 1
- SimpleGraph.not_isTutteViolator_of_isPerfectMatchingproof · cited by 1