
theorem
for R being comRing,
    p being Polynomial of R st deg p < 2
for a being Element of R ex y,z being Element of R st eval(p,a) = y + a * z
proof
let R be comRing; let p be Polynomial of R;
assume A: deg p < 2;
let a be Element of R;
consider y,z being Element of R such that B: p = <%y,z%> by A,deg2;
take y,z;
thus eval(p,a) = y + z * a by B,POLYNOM5:44 .= y + a * z by GROUP_1:def 12;
end;
