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There are two ways how to read \def\def@man{...}. If catcode of @ is set to 11 (letter) at the time the text above is read from the file then the control sequence def@man is defined here. If catcode of @ is set to 12 (other, this is more usual) then \def\def@man{...} redefines the TeX primitive \def as a macro with mandatory separator @man and (probably) ...


Generally you'll see these \DeclareOption{<opt>}{<stuff>} declarations in style (.sty) and class (.cls) files. The allow the user to use the style/package or class with certain parameter specification which could influence the usage. In the above case, the option man is declared that \defines \def@man to be \@manmode, or in short ...

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