Let z be given.

Assume Hz.

Apply octonion_E z Hz to the current goal.

Let x be given.

Assume Hx.

Let y be given.

Assume Hy.

Assume Hzxy: z = pa x y.

We will prove OSNo z.

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

Apply OSNo_I to the current goal.

An exact proof term for the current goal is quaternion_HSNo x Hx.

An exact proof term for the current goal is quaternion_HSNo y Hy.

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