cases P
α : Type u_1
inst✝ : CompleteLattice α
s x y z : α
P✝ P Q : Partition s
hP : ∀ (x : α), x ∈ P ↔ x ∈ Q
⊢ P = Q
case mk
α : Type u_1
inst✝ : CompleteLattice α
s x y z : α
P Q : Partition s
parts✝ : Set α
setIndependent✝ : CompleteLattice.SetIndependent parts✝
bot_not_mem✝ : ⊥ ∉ parts✝
sSup_eq'✝ : sSup parts✝ = s
hP :
  ∀ (x : α),
    x ∈ { parts := parts✝, setIndependent := setIndependent✝, bot_not_mem := bot_not_mem✝, sSup_eq' := sSup_eq'✝ } ↔
      x ∈ Q
⊢ { parts := parts✝, setIndependent := setIndependent✝, bot_not_mem := bot_not_mem✝, sSup_eq' := sSup_eq'✝ } = Q