simp only [← and_assoc]
case cons.h
α : Type u
inst✝ : DecidableEq α
a b : α
x : Array α
IH : Nodup (push x a) ↔ Nodup x ∧ ¬a ∈ x
⊢ ¬b = a ∧ Nodup x ∧ ¬a ∈ x ↔ Nodup x ∧ ¬a = b ∧ ¬a ∈ x
case cons.h
α : Type u
inst✝ : DecidableEq α
a b : α
x : Array α
IH : Nodup (push x a) ↔ Nodup x ∧ ¬a ∈ x
⊢ (¬b = a ∧ Nodup x) ∧ ¬a ∈ x ↔ (Nodup x ∧ ¬a = b) ∧ ¬a ∈ x