 reserve o for object;
 reserve F for non almost_trivial Field;
 reserve x,a for Element of F;
reserve n for non zero Nat;

theorem Th18:
   for R being Ring, p being Polynomial of R for n being Nat holds p <> n
   proof
     let R be Ring, p be Polynomial of R; let u be Nat;
     reconsider n = u as Element of NAT by ORDINAL1:def 12;
     now assume
A1:    p = n;
       dom p = NAT by FUNCT_2:def 1; then
       consider i being Nat such that
A2:    i = [n,p.n] & i < n by A1;
       thus contradiction by A2;
     end;
     hence thesis;
   end;
