Theorems · Theorem · combinatorics
Finpartition.IsEquipartition.card_part_le_average_add_one
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Finset α} {P : Finpartition s},
P.IsEquipartition → t ∈ P.parts → t.card ≤ s.card / P.parts.card + 1- Defined in
- Mathlib.Order.Partition.Equipartition
- Cited by
- 3 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.le_add_oneproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Finpartition.IsEquipartition.card_biUnion_offDiag_le'proof · cited by 1
- Finpartition.IsEquipartition.card_interedges_sparsePairs_le'proof · cited by 1
- Finpartition.IsEquipartition.sum_nonUniforms_lt'proof · cited by 1