Apply HSNo_proj0proj1_split (j '') (:-: j) (HSNo_conj_HSNo j HSNo_Quaternion_j) (HSNo_minus_HSNo j HSNo_Quaternion_j) to the current goal.
We will prove p0 (j '') = p0 (:-: j).
rewrite the current goal using conj_HSNo_proj0 j HSNo_Quaternion_j (from left to right).
rewrite the current goal using minus_HSNo_proj0 j HSNo_Quaternion_j (from left to right).
We will prove p0 j ' = - p0 j.
rewrite the current goal using HSNo_p0_j (from left to right).
We will prove 0 ' = - 0.
rewrite the current goal using minus_CSNo_0 (from left to right).
An exact proof term for the current goal is conj_CSNo_id_SNo 0 SNo_0.
We will prove p1 (j '') = p1 (:-: j).
rewrite the current goal using conj_HSNo_proj1 j HSNo_Quaternion_j (from left to right).
rewrite the current goal using minus_HSNo_proj1 j HSNo_Quaternion_j (from left to right).
We will prove - p1 j = - p1 j.
Use reflexivity.
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