reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;

theorem
  for f,g being Morphism of C st dom(g) = cod(f) holds dom(g(*)f) =
  dom(f) & cod(g(*)f) = cod(g) by Def5;
