Theorems · Theorem · combinatorics
Finpartition.IsEquipartition.average_le_card_part
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Finset α} {P : Finpartition s},
P.IsEquipartition → t ∈ P.parts → s.card / P.parts.card ≤ t.card- Defined in
- Mathlib.Order.Partition.Equipartition
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.cardstatement and proof · cited by 2,327
- Finpartitionstatement and proof · cited by 199
- Finpartition.partsstatement and proof · cited by 184
- Finpartition.IsEquipartitionstatement and proof · cited by 45
- Finpartition.sum_card_partsproof · cited by 5
- Finset.EquitableOn.leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SzemerediRegularity.pow_mul_m_le_card_partproof · cited by 0