The one walking goes in front of the funeral and the one riding behind it

It is narrated from Sayyiduna al-Mughirah bin Shu'bah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "The one walking should walk in front of the funeral and the one riding behind it, and the funeral prayer is also to be offered over a deceased child."
This hadith is sahih (authentic) on the condition of Bukhari, but the two Shaykhs did not record it.

It is narrated from Sayyiduna Thawban (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) accompanied a funeral. A mount was brought to him, but he refused to ride it. Then, when he was about to return after finishing with the funeral, a mount was brought and he rode it. He was asked about this, and he said: "The angels were walking, so it was not fitting for me to ride while they were walking. Then when they went away (or he said: ascended), I rode."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it, and it has a supporting narration (shahid) whose wording is clearer.

It is narrated from Sayyiduna Thawban (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) went out with a funeral and saw some people riding. He said: "Do you not feel ashamed? The angels of Allah are on foot while you are on the backs of animals!"