62 \begin{abstract}

    62 \begin{abstract}

    63 Higher-Order Logic (HOL) is based on a small logic kernel, whose only

    63 Higher-Order Logic (HOL) is based on a small logic kernel, whose only

    64 mechanism for extension is the introduction of safe definitions and of

    64 mechanism for extension is the introduction of safe definitions and of

    65 non-empty types. Both extensions are often performed in quotient

    65 non-empty types. Both extensions are often performed in quotient

    66 constructions. To ease the work involved with such quotient constructions, we

    66 constructions. To ease the work involved with such quotient constructions, we

    68 package by Homeier. In doing so we extended his work in order to deal with 

    69 package by Homeier. In doing so we extended his work in order to deal with 

    69 compositions of quotients and also specified completely the procedure 

    70 compositions of quotients and also specified completely the procedure 

    70 of lifting theorems from the raw level to the quotient level.

    71 of lifting theorems from the raw level to the quotient level.

    71 The importance for theorem proving is that many formal

    72 The importance for theorem proving is that many formal

    72 verifications, in order to be feasible, require a convenient reasoning infrastructure 

    73 verifications, in order to be feasible, require a convenient reasoning infrastructure 

    79 

    80 

    80 % generated text of all theories

    81 % generated text of all theories

    81 \input{session}

    82 \input{session}

    82 

    83 

    83 % optional bibliography

    84 % optional bibliography

    84 \bibliographystyle{abbrv}

    87 \bibliographystyle{abbrv}

    85 \bibliography{root}

    88 \bibliography{root}

    86 

    89 

    87 \end{document}

    90 \end{document}

    88 

    91