The term 'Han-in(桓因)' in Samgukyusa(The Overlooked Historic Records of Three Countries, 三國遺事) doesn't originated from Buddhism, but is the Chinese transcription of 'Haneunim', which Koreans has revered as God for ages. The religious belief in 'Han-in', that is, 'Haneunim' was revealed as 'Hanalnim' of Donghak by Choe Suwoon(崔水雲) late in the 19th century.
I call the records concerning Gochosun in Samgukyusa 'Handangosa'(The Brief Records about Han-in, Han-ung(桓雄) and Dangun(檀君), 桓檀古事). According to Handangosa, Han-in and Han-ung symbolize the heaven or the being of heaven, and a bear and a tiger the earth or the being of earth. And then, Dangun is a new human, which is based on the being of earth, and in which the spirit of heaven is implanted. It means that humans are born on the basis of the heaven and the earth. Therefore, it suggests that humans cannot leave the heaven and the earth. Besides, it implies that the heaven and the earth also have established responsibility upon humans.
First, the establishment of relationship between Han-in and Han-ung(桓雄) is important. We can realized that the relationship between father and son is emphasized ethically through the term 'Bujijaeui'(Father God knows his son's will and let him go to the earth, 父知子意). 'Bujijaeui' also appeared in Donghak. Suwoon met God, who gave him Chondo (The Heavenly Way, 天道).
Second, Cheonbuin(A Thing, on which the divine world of the heaven is carved, 天符印) and Juwonyuing(Praying for Pregnancy by reciting a charm, 呪願有孕) have to be thoguht together. The relation of the two is the relation between Bu(符) and Ju(呪). In other words, when it is understood as the relation betweem Cheonbu(天符) and Jumun(呪文), it is connected with Youngbu(靈符) and Jumun(呪文) in Donghak.
Third, the position of Han-ung in the term 'Hanungcheonwang' is an issue. Cheonwang means an authority acting as a intermediary between gods and men. Suwoon called himself "Cheonhwangssi(天皇氏) of Hucheon(後天)" and emphasized himself as the spiritual subject of new cosmic creation.
Fourth, the thought about number three can be found. Cheonbuin Samgae(三箇), three years, three masters[Pungbaek(風伯The Master of the Wind), Usa(雨師The Master of the Rain), Unsa(雲師The Master of the Cloud)], Samchilil(三七日) and others all show number three. The thought about number three in Donghak can be found in the thought of unity of Confucianism, Buddhism, and Taoism.
Last, the relation between the thought of Handan and Suwoongyo is a problem. There is Cheondan(天壇), on which Hanalnim and the heavenly hosts are worshiped in Suwoongyo. Also, Suwoongyo worships a mortuary tablet of Dangun. These have a significant meaning. If we pursue the origin of Cheondan retroactively, we can reach Chamseongdan(祭天壇) in Mt. Mani in Ganghwado, which seems to be build in the age of Dangun. I guess it means that Cheondan of Suwoongyo(Registered as a tangible cultural asset) succeed to the ritual of revering the heaven, which is handed down since the age of Dangun. It seems that Hanalnim worshiped on Cheondan and Ilwolsang(日月像) is related to Cheonbusamin(天符 3印) found in Samgukyusa.