
theorem exevalminus2:
for R being Ring,
    S being RingExtension of R
for a being Element of S,
    p,q being Polynomial of R
holds Ext_eval(p-q,a) = Ext_eval(p,a) - Ext_eval(q,a)
proof
let R be Ring, S be RingExtension of R;
let a be Element of S, p,q be Polynomial of R;
R is Subring of S by FIELD_4:def 1;
hence Ext_eval(p-q,a) = Ext_eval(p,a) + Ext_eval(-q,a) by ALGNUM_1:15
                     .= Ext_eval(p,a) - Ext_eval(q,a) by exevalminus;
end;
