
theorem
for p be non constant with_positive_coefficients real Polynomial of F_Complex
st [even_part(p),odd_part(p)] is one_port_function &
   degree([even_part(p),odd_part(p)]) = degree p
holds p is Hurwitz
proof
let p be non constant with_positive_coefficients
                                   real Polynomial of F_Complex;
set e = even_part p, o = odd_part p;
set f = [e,o];
assume A1: [e,o] is one_port_function & degree([e,o]) = degree p;
A2: f is non zero;
degree f = max ( degree f`1, degree f`2 ) by A1,Th23;
then f is irreducible by A2,RATFUNC1:30;
then e + o is Hurwitz by A1,Th30;
hence p is Hurwitz by Th9;
end;
