Theorems · Theorem · order theory
Setoid.eq_of_mem_classes
∀ {α : Type u_1} {r : Setoid α} {x : α} {b : Set α},
b ∈ r.classes → x ∈ b → ∀ {b' : Set α}, b' ∈ r.classes → x ∈ b' → b = b'If x ∈ α is in 2 equivalence classes, the equivalence classes are equal.
- Defined in
- Mathlib.Data.Setoid.Partition
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Setoid.classesstatement and proof · cited by 17
- Setoid.eq_of_mem_eqv_classproof · cited by 3
- Setoid.classes_eqv_classesproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Setoid.mkClasses_classesproof · cited by 0