Theorems · Theorem · combinatorics
Finpartition.IsEquipartition.exists_partPreservingEquiv
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {P : Finpartition s},
P.IsEquipartition → ∃ f, ∀ (a b : ↥s), P.part ↑a = P.part ↑b ↔ ↑(f a) % P.parts.card = ↑(f b) % P.parts.cardGiven a finset equipartitioned into k parts, its elements can be enumerated such that
elements in the same part have congruent indices modulo k.
- Defined in
- Mathlib.Order.Partition.Equipartition
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Equivstatement and proof · cited by 8,337
- Equiv.symmproof · cited by 3,681
- Finset.cardstatement and proof · cited by 2,327
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- LT.lt.ne'proof · cited by 1,417
- Function.Bijectiveproof · cited by 863
- LE.le.trans_ltproof · cited by 795
- Equiv.injectiveproof · cited by 464
- mul_le_mul'proof · cited by 274
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraphproof · cited by 3