Theorems · Theorem · combinatorics
Equiv.Perm.exists_map_finset_eq
∀ {β : Type u_2} (s t : Finset β), s.card = t.card → ∃ σ, Finset.map (Equiv.toEmbedding σ) s = tAny two same-cardinality finsets are related by a permutation.
- Defined in
- Mathlib.Logic.Equiv.Fintype
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Finsetstatement and proof · cited by 13,712
- Finset.cardstatement and proof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Finset.mapstatement and proof · cited by 747
- Equiv.injectiveproof · cited by 464
- Equiv.toEmbeddingstatement and proof · cited by 254
- Subtype.val_injectiveproof · cited by 232
- Finset.card_mapproof · cited by 114
- Finset.eq_of_subset_of_card_leproof · cited by 34
- Finset.mem_mapproof · cited by 32
- Equiv.Perm.exists_extending_pairproof · cited by 2
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