have hzmem : z ∈ A := by
  simp only [Set.mem_setOf_eq]
  rw [zmul]
x : ↑N0
A : Set ↑N0 := {x | mul (S z, x) = x}
⊢ mul (S z, x) = x
x : ↑N0
A : Set ↑N0 := {x | mul (S z, x) = x}
hzmem : z ∈ A
⊢ mul (S z, x) = x