Theorems · Theorem · order theory
Finpartition.nonempty_of_mem_parts
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} (P : Finpartition s) {a : Finset α}, a ∈ P.parts → a.Nonempty- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 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.
Cites6
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.Nonemptystatement · cited by 1,001
- Finpartitionstatement and proof · cited by 199
- Finpartition.partsstatement and proof · cited by 184
- Finset.nonempty_iff_ne_emptyproof · cited by 34
- Finpartition.ne_botproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- Finpartition.equitabilise_auxproof · cited by 3
- Finpartition.IsEquipartition.card_interedges_sparsePairs_le'proof · cited by 1
- Finpartition.part_surjOnproof · cited by 1
- SimpleGraph.IsTuranMaximal.isEquipartitionproof · cited by 1