reserve x for object, X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for complex-valued Function;
reserve r,p for Complex;

theorem
  (f/g)/(f1/g1) = (f(#)(g1|dom(g1^)))/(g(#)f1)
proof
  thus (f/g)/(f1/g1) = (f/g)(#)((f1/g1)^) by Th31
    .= (f/g)(#)(((g1|dom(g1^)))/f1) by Th35
    .= (f(#)(g1|dom(g1^)))/(g(#)f1) by Th34;
end;
