theorem
  c1*(c2*z) = (c1*c2)*z
proof
  thus (c1*c2)*z = multcomplex[;](multcomplex.(c1,c2),id COMPLEX)*z by
BINOP_2:def 5
    .= multcomplex[;](c1,multcomplex[;](c2,id COMPLEX))*z by FUNCOP_1:62
    .= (multcomplex[;](c1,id COMPLEX)*multcomplex[;](c2,id COMPLEX))*z by
FUNCOP_1:55
    .= c1*(c2*z) by RELAT_1:36;
end;
