We prove the intermediate claim Li5: OSNo i5.
An exact proof term for the current goal is OSNo_Octonion_i5.
We prove the intermediate claim Li2: OSNo i2.
An exact proof term for the current goal is OSNo_Quaternion_j.
We prove the intermediate claim Li3: OSNo i3.
An exact proof term for the current goal is OSNo_Octonion_i3.
We prove the intermediate claim Li2i5: OSNo (i2 ⨯ i5).
An exact proof term for the current goal is OSNo_mul_OSNo i2 i5 ?? ??.
Apply OSNo_proj0proj1_split (i2 ⨯ i5) (:-: i3) ?? (OSNo_minus_OSNo i3 ??) to the current goal.
rewrite the current goal using minus_OSNo_proj0 i3 ?? (from left to right).
rewrite the current goal using OSNo_p0_i3 (from left to right).
rewrite the current goal using mul_OSNo_proj0 i2 i5 ?? ?? (from left to right).
rewrite the current goal using OSNo_p0_i5 (from left to right).
rewrite the current goal using OSNo_p1_i5 (from left to right).
rewrite the current goal using OSNo_p0_j (from left to right).
rewrite the current goal using OSNo_p1_j (from left to right).
We will prove j * 0 + - ((- k) ' * 0) = - 0.
rewrite the current goal using mul_HSNo_0R j HSNo_Quaternion_j (from left to right).
rewrite the current goal using mul_HSNo_0R ((- k) ') (HSNo_conj_HSNo (- k) (HSNo_minus_HSNo k HSNo_Quaternion_k)) (from left to right).
rewrite the current goal using minus_HSNo_0 (from left to right).
An exact proof term for the current goal is add_HSNo_0L 0 HSNo_0.
rewrite the current goal using minus_OSNo_proj1 i3 ?? (from left to right).
rewrite the current goal using OSNo_p1_i3 (from left to right).
rewrite the current goal using mul_OSNo_proj1 i2 i5 ?? ?? (from left to right).
rewrite the current goal using OSNo_p0_i5 (from left to right).
rewrite the current goal using OSNo_p1_i5 (from left to right).
rewrite the current goal using OSNo_p0_j (from left to right).
rewrite the current goal using OSNo_p1_j (from left to right).
We will prove (- k) * j + 0 * 0 ' = - (- i).
rewrite the current goal using conj_HSNo_id_SNo 0 SNo_0 (from left to right).
rewrite the current goal using mul_HSNo_0L 0 HSNo_0 (from left to right).
rewrite the current goal using minus_mul_HSNo_distrL k j HSNo_Quaternion_k HSNo_Quaternion_j (from left to right).
rewrite the current goal using Quaternion_k_j (from left to right).
rewrite the current goal using minus_HSNo_invol i HSNo_Complex_i (from left to right).
An exact proof term for the current goal is add_HSNo_0R i HSNo_Complex_i.
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