
theorem
for R being domRing
for p being non zero Polynomial of R holds deg(<%0.R,1.R%> *' p) = deg(p) + 1
proof
let R be domRing, p be non zero Polynomial of R;
B: len <%0.R,1.R%> = 2 by POLYNOM5:40; then
A: <%0.R,1.R%> <> 0_.(R) by POLYNOM4:3;
C: deg <%0.R,1.R%> = 2 - 1 by B,HURWITZ:def 2;
thus deg(<%0.R,1.R%> *' p) = deg(p) + 1 by C,A,HURWITZ:23;
end;
