Theorems · Theorem · order theory
Partition.nonempty_of_mem
∀ {α : Type u_1} {u t : Set α} {P : Partition u}, t ∈ P → t.Nonempty- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement · cited by 2,627
- Partitionstatement and proof · cited by 91
- Partition.ne_bot_of_memproof · cited by 4
- Set.notMem_singleton_emptyproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Partition.repproof · cited by 7
- Partition.rep_memproof · cited by 3
- Partition.subset_sUnion_and_mem_iff_memproof · cited by 1
- Partition.rel_le_iff_leproof · cited by 0