We prove the intermediate claim Li4: OSNo i4.
An exact proof term for the current goal is OSNo_Quaternion_k.
We prove the intermediate claim Li6: OSNo i6.
An exact proof term for the current goal is OSNo_Octonion_i6.
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 Li4i6: OSNo (i4 ⨯ i6).
An exact proof term for the current goal is OSNo_mul_OSNo i4 i6 ?? ??.
Apply OSNo_proj0proj1_split (i4 ⨯ i6) i3 ?? ?? to the current goal.
rewrite the current goal using OSNo_p0_i3 (from left to right).
rewrite the current goal using mul_OSNo_proj0 i4 i6 ?? ?? (from left to right).
rewrite the current goal using OSNo_p0_k (from left to right).
rewrite the current goal using OSNo_p1_k (from left to right).
rewrite the current goal using OSNo_p0_i6 (from left to right).
rewrite the current goal using OSNo_p1_i6 (from left to right).
We will prove k * 0 + - ((- j) ' * 0) = 0.
rewrite the current goal using mul_HSNo_0R k HSNo_Quaternion_k (from left to right).
rewrite the current goal using mul_HSNo_0R ((- j) ') (HSNo_conj_HSNo (- j) (HSNo_minus_HSNo j HSNo_Quaternion_j)) (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 OSNo_p1_i3 (from left to right).
rewrite the current goal using mul_OSNo_proj1 i4 i6 ?? ?? (from left to right).
rewrite the current goal using OSNo_p0_k (from left to right).
rewrite the current goal using OSNo_p1_k (from left to right).
rewrite the current goal using OSNo_p0_i6 (from left to right).
rewrite the current goal using OSNo_p1_i6 (from left to right).
We will prove (- j) * k + 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 j k HSNo_Quaternion_j HSNo_Quaternion_k (from left to right).
rewrite the current goal using Quaternion_j_k (from left to right).
An exact proof term for the current goal is add_HSNo_0R (- i) (HSNo_minus_HSNo i HSNo_Complex_i).
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