Theorems · Theorem · order theory
Partition.mem_iff_exists
∀ {α : Type u_1} {x : α} {u : Set α} {P : Partition u}, x ∈ u ↔ ∃ t ∈ P, x ∈ t- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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
- Partitionstatement and proof · cited by 91
- Set.mem_sUnionproof · cited by 11
- Partition.subset_of_memproof · cited by 7
- Partition.sUnion_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Partition.mem_iff_mem_partOf_memproof · cited by 2