Theorems · Theorem · order theory
memPartitionSet_eq_iff
∀ {α : Type u_1} {f : ℕ → Set α} {n : ℕ} (a : α) {s : Set α}, s ∈ memPartition f n → (memPartitionSet f n a = s ↔ a ∈ s)- Defined in
- Mathlib.Data.Set.MemPartition
- Cited by
- 3 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.
Cites8
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
- Disjointproof · cited by 2,201
- Set.not_disjoint_iff_nonempty_interproof · cited by 29
- memPartitionstatement and proof · cited by 20
- memPartitionSetstatement and proof · cited by 12
- memPartitionSet_memproof · cited by 5
- disjoint_memPartitionproof · cited by 3
- mem_memPartitionSetproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.measurable_memPartitionSet_subtypeproof · cited by 2
- memPartitionSet_of_memproof · cited by 1
- MeasurableSpace.countablePartitionSet_eq_iffproof · cited by 0