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Theorems · Theorem · logic and foundations

Function.Embedding.total

∀ (α : Type u) (β : Type v), Nonempty (α ↪ β) ∨ Nonempty (β ↪ α)

The cardinals are totally ordered. See Cardinal.conditionallyCompleteLinearOrderBot for (one of) the lattice instance.

Defined in
Mathlib.SetTheory.Cardinal.SchroederBernstein
Cited by
1 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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nonempty_embedding_to_cardinal · cited by 0nonempty_embedding_to_car…Function.Embedding · cited by 988Function.EmbeddingEquiv.ulift · cited by 115Equiv.uliftFunction.Embedding.congr · cited by 5Embedding.congrFunction.Embedding.min_injective · cited by 2Embedding.min_injectiveEmbedding.totalCITED BYCITES

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Cited by1

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