Let x be given.

Assume Hx: x ∈ real.

We will prove x ∈ complex.

rewrite the current goal using SNo_pair_0 x (from right to left).

We will prove pa x 0 ∈ complex.

Apply complex_I to the current goal.

An exact proof term for the current goal is Hx.

An exact proof term for the current goal is real_0.

∎