
theorem Th8:
for L being add-associative right_zeroed right_complementable
            unital right-distributive non empty doubleLoopStr
for p being Polynomial of L st deg p = 0
for x being Element of L holds eval(p,x) <> 0.L
proof
let L be add-associative right_zeroed right_complementable
         unital right-distributive non empty doubleLoopStr;
let p be Polynomial of L;
assume A1: deg p = 0;
let x be Element of L;
assume eval(p,x) = 0.L;
then x is_a_root_of p by POLYNOM5:def 7;
then p is with_roots by POLYNOM5:def 8;
hence contradiction by A1,HURWITZ:24;
end;
