well founded

/ˌwɛlˈfaʊndɪd/
adjective
  1. Based on good evidence or strong reasons; justified.
    • His suspicion that someone had been in his office was well-founded; the lock was broken.
    • The scientist's theory proved well-founded after years of research.
    • Her fear of flying was well-founded after she read about the mechanical issues.
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