reserve I for set,
  x,x1,x2,y,z for set,
  A for non empty set;
reserve C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,g,h,i,j,k,p1,p2,q1,q2,i1,i2,j1,j2 for Morphism of C;
reserve f for Morphism of a,b,
        g for Morphism of b,a;
reserve g for Morphism of b,c;
reserve f,g for Morphism of C;

theorem
  for f being Morphism of a,b st a is initial holds init(a,b) = f
proof
  let f be Morphism of a,b;
  assume
A1: a is initial;
  then Hom(a,b) <> {};
  then dom f = a & cod f = b by CAT_1:5;
  hence thesis by A1,Th39;
end;
