Theorems · Theorem · order theory
Setoid.eq_of_mem_eqv_class
∀ {α : Type u_1} {c : Set (Set α)},
(∀ (a : α), ∃! b, b ∈ c ∧ a ∈ b) → ∀ {x : α} {b b' : Set α}, b ∈ c → x ∈ b → b' ∈ c → x ∈ b' → b = b'If x ∈ α is in 2 elements of a set of sets partitioning α, those 2 sets are equal.
- Defined in
- Mathlib.Data.Setoid.Partition
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- ExistsUniquestatement and proof · cited by 268
- ExistsUnique.uniqueproof · cited by 42
Cited by3
Results whose statement or proof uses this declaration.
- Setoid.eq_eqv_class_of_memproof · cited by 3
- Setoid.eq_of_mem_classesproof · cited by 1
- Setoid.eqv_classes_disjointproof · cited by 1