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    No valid proof can consist solely of empty sequents, sinc... — Carmelics
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    Supports→The empty sequent is not provable

    No valid proof can consist solely of empty sequents, since every proof must contain axioms

    Proof of definition segmentsTruth & Knowledge
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    A cut-free derivation of the empty sequent can contain only empty sequentsIf the empty sequent were provable, it would have a cut-free derivation by the H...The empty sequent is not provable

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    The empty sequent is not provable82%If the empty sequent were provable, it would have a cut-free derivatio...80%A cut-free derivation of the empty sequent can contain only empty sequ...80%The Gödel completeness theorem establishes that the set of all valid f...78%

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    Proof: Assume that the empty sequent is provable; then, according to the Hauptsatz it has a cut-free derivation \(\cD\). The previous corollary assures us that only empty sequents can occur in \(\cD\); but such a \(\cD\) does not exist since every proof must contain axioms. \(\qed\)

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