
theorem Th25:
for L being add-associative right_zeroed right_complementable Abelian
            well-unital non degenerated doubleLoopStr
for p being odd Polynomial of L
for x being Element of L
holds eval(p,-x) = - eval(p,x)
proof
let L be add-associative right_zeroed right_complementable Abelian
         well-unital non degenerated doubleLoopStr;
let p be odd Polynomial of L;
let x be Element of L;
A1: Polynomial-Function(L,p) is odd by Def6;
thus eval(p,-x) = Polynomial-Function(L,p).(-x) by POLYNOM5:def 13
               .= - Polynomial-Function(L,p).x by A1
               .= - eval(p,x) by POLYNOM5:def 13;
end;
