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Theorems · Theorem · logic and foundations

Finite.card_eq_zero_of_embedding

∀ {α : Type u_1} {β : Type u_2} [Nonempty α] (f : α ↪ β), Nat.card α = 0 → Nat.card β = 0

NB: Nat.card is defined to be 0 for infinite types.

Defined in
Mathlib.SetTheory.Cardinal.NatCard
Cited by
4 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSubgroup.relIndex_eq_zero_of_le_right · cited by 5AddSubgroup.relIndex_eq_z…Subgroup.relIndex_eq_zero_of_le_right · cited by 5Subgroup.relIndex_eq_zero…AddSubgroup.relIndex_iInf_ne_zero · cited by 1AddSubgroup.relIndex_iInf…Subgroup.relIndex_iInf_ne_zero · cited by 1Subgroup.relIndex_iInf_ne…Function.Embedding · cited by 988Function.EmbeddingNat.card · cited by 844Nat.cardFunction.Embedding.inj' · cited by 29Embedding.inj'Finite.card_eq_zero_of_injective · cited by 1Finite.card_eq_zero_of_in…Finite.card_eq_zero_of_embedd…CITED BYCITES

Cites4

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Cited by4

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