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= incontrovertible, without a shadow of a doubt, beyond a shadow of a doubt

Ex. Let me take an absolutely incontrovertible example.

Ex. This is without a shadow of a doubt one of the weirdest and probably disturbing postings I have ever had the pleasure to read.

Ex. The film proves beyond a shadow of a doubt that the official story is hogwash and that all the evidence points towards an inside job.

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= incontrovertible, without a shadow of a doubt, beyond a shadow of a doubt

Ex: Let me take an absolutely incontrovertible example.

Ex: This is without a shadow of a doubt one of the weirdest and probably disturbing postings I have ever had the pleasure to read.

Ex: The film proves beyond a shadow of a doubt that the official story is hogwash and that all the evidence points towards an inside job.