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    \card{convention}{definition style}{

    In this document, we unify the informal mathematical language for a definition to:

    \optional{Let \placeholder{\(X\)} be a \placeholder{\vocab{concept \(X\)}}. }

    A \newvocab{\placeholder{concept \(Z\)}} is a set/pair/triple/tuple \((Z, \mathtt {op}, ...)\), satisfying:

    1. \placeholder{\(Z\)} is a \placeholder{\vocab{concept \(Y\)}} \optional{ over \placeholder{\(X\)} under \placeholder{op} }.
    2. \placeholder{formula} for all \placeholder{elements in \(Z\)} \optional{(\vocab{ \placeholder{property} })}.
    3. \optional{for each \placeholder{element} in \placeholder{\vocab{concept \(X\)}}, } there exists \placeholder{element} such that \placeholder{formula} for all \placeholder{elements in concept \(Z\)}.
    4. \optional{\placeholder{op} is called \placeholder{\vocab{op name}}, }for all \placeholder{elements in \(Z\)}, we have
      1. \placeholder{formula}
      2. \placeholder{formula}
      \optional{(\vocab{ \placeholder{property} })}.

    By default, \placeholder{\(X\)} is a set, \placeholder{op} is a binary operation on \placeholder{\(X\)}.

    }