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 Li6: OSNo i6.
An exact proof term for the current goal is OSNo_Octonion_i6.
We prove the intermediate claim Li0: OSNo i0.
An exact proof term for the current goal is OSNo_Octonion_i0.
We prove the intermediate claim Li2i6: OSNo (i2 ⨯ i6).
An exact proof term for the current goal is OSNo_mul_OSNo i2 i6 ?? ??.
Apply OSNo_proj0proj1_split (i2 ⨯ i6) i0 ?? ?? to the current goal.
rewrite the current goal using OSNo_p0_i0 (from left to right).
rewrite the current goal using mul_OSNo_proj0 i2 i6 ?? ?? (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).
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 * 0 + - ((- j) ' * 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 ((- 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_i0 (from left to right).
rewrite the current goal using mul_OSNo_proj1 i2 i6 ?? ?? (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).
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) * j + 0 * 0 ' = 1.
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 j HSNo_Quaternion_j HSNo_Quaternion_j (from left to right).
rewrite the current goal using Quaternion_j_sqr (from left to right).
rewrite the current goal using minus_HSNo_invol 1 HSNo_1 (from left to right).
An exact proof term for the current goal is add_HSNo_0R 1 HSNo_1.
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