reserve n for Nat;

theorem lem1c:
for n being odd Nat
holds eval(npoly(F_Real,n),-1.F_Real) = 0.F_Real
proof
let n be odd Nat;
consider k being Nat such that H: n-1 = 2 * k by ABIAN:def 2;
A: k is Element of NAT by ORDINAL1:def 12;
(-1.F_Real)|^n = (power F_Real).(-1.F_Real,2*k+1) by H
              .= -1_F_Real by A,HURWITZ:4
              .= -1.F_Real;
hence eval(npoly(F_Real,n),-1.F_Real) = -1.F_Real + 1.F_Real by lem1a
                                     .= 0.F_Real;
end;
