Theorems · Theorem · order theory
Finpartition.part_eq_empty
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} (P : Finpartition s) {a : α}, P.part a = ∅ ↔ a ∉ s- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 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.
Cites5
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
- Finpartitionstatement and proof · cited by 199
- Finpartition.partstatement and proof · cited by 22
- Finpartition.part_memproof · cited by 5
- Finpartition.ne_emptyproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Finpartition.part_nonemptyproof · cited by 1
- Finpartition.mem_part_selfproof · cited by 1
- Finpartition.part_subsetproof · cited by 0