reserve X for BCI-algebra;
reserve x,y,z for Element of X;
reserve i,j,k,l,m,n for Nat;
reserve f,g for sequence of the carrier of X;

theorem
  Polynom (m,n,x,y) = (((Polynom (0,0,x,y),(x\y)) to_power m),(y\x)) to_power n
proof
  (Polynom (0,0,x,y),(x\y)) to_power m = ((x\(x\y)),(x\y)) to_power m by Th7
    .= ((x,(x\y)) to_power m) \ (x\y) by BCIALG_2:7
    .= (x,(x\y)) to_power (m+1) by BCIALG_2:4;
  hence thesis;
end;
