reserve A for non empty set,
  a,b,x,y,z,t for Element of A,
  f,g,h for Permutation of A;

theorem
  (f*g)\h = (f\h)*(g\h)
proof
  thus (f*g)\h = (h*(f*((id A)*g)))*h" by FUNCT_2:17
    .= (h*(f*((h"*h)*g)))*h" by FUNCT_2:61
    .= (h*(f*(h"*(h*g))))*h" by RELAT_1:36
    .= (h*((f*h")*(h*g)))*h" by RELAT_1:36
    .= ((h*(f*h"))*(h*g))*h" by RELAT_1:36
    .= (h*(f*h"))*((h*g)*h") by RELAT_1:36
    .= (f\h)*(g\h) by RELAT_1:36;
end;
