Je was op zoek naar: substantiated (Engels - Japans)

they substantiated their claim by producing dated receipts.
彼らは日付のついた領収書をみせて自分たちの主張を立証した。

that assumption is further substantiated by the presence of a dog at the scene of the crime.
否定はしないが 仮定の裏付けには十分だ

mr. moran, your claims about moriarty cannot be substantiated and are of no interest.
モランさん モリアティーについての君の話は 証拠が無いし 興味もわかないね