simp only [Subtype.coe_eta, Subtype.coe_prop, exists_const, iff_true] at heq
x : ↑N0
A : Set ↑N0 := {x | mul (z, x) = z}
hzmem : z ∈ A
hind : ∀ n ∈ A, S n ∈ A
heq : (∃ (x_1 : ↑x ∈ N0), mul (z, { val := ↑x, property := (_ : ↑x ∈ N0) }) = z) ↔ ↑x ∈ N0
⊢ mul (z, x) = z
x : ↑N0
A : Set ↑N0 := {x | mul (z, x) = z}
hzmem : z ∈ A
hind : ∀ n ∈ A, S n ∈ A
heq : mul (z, x) = z
⊢ mul (z, x) = z