How to say prove that p is a poset. in Japanese

1)P(P) (n) p/pが(ga) (prt) indicates sentence subject/indicates possessive/but/however/still/and半順序no dictionary result, likely a conjigated verbno dictionary result, likely a conjigated verb集合集合(shuugou) (n,vs,adj-no) gathering/assembly/meeting/setであるである(dearu) (v5r-i) to beことこと(koto) (prt) particle indicating a command/particle indicating mild enthusiasm/particle indicating a gentle interrogative/particle used to soften a judgment or conclusionを(wo) (prt) indicates direct object of action/indicates subject of causative expression/indicates an area traversed/indicates time over which action takes place/indicates point of departure or separation of action/indicates object of desire, like, hate,証明せno dictionary result, likely a conjigated verbno dictionary result, likely a conjigated verbよ(yo) (num) four。(。) Japanese period "."    
P ga hanjunjo shuugou dearukotowo shoumeise yo 。
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Translation by blay_paul
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