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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

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