Let x and y be given.

Assume Hx: SNo x.

Assume Hy: SNo y.

Assume Hxy: - x < y.

We will prove - y < x.

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

We will prove - y < - - x.

Apply minus_SNo_Lt_contra (- x) y (SNo_minus_SNo x Hx) Hy to the current goal.

We will prove - x < y.

An exact proof term for the current goal is Hxy.

∎