reserve i,j,n,n1,n2,m,k,l,u for Nat,
        i1,i2,i3,i4,i5,i6 for Element of n,
        p,q for n-element XFinSequence of NAT,
        a,b,c,d,e,f for Integer;

theorem Th7:
  for n being Ordinal,p being Polynomial of n, F_Real st
    |.p.| = 0_(n,F_Real) holds p = 0_(n,F_Real)
proof
  let n be Ordinal,p be Polynomial of n, F_Real;
  assume
A1: |.p.| = 0_(n,F_Real);
  now let b be Element of Bags n;
    |. p .b .| = |.p.| .b by Def1
      .= 0 by A1;
    hence p.b = 0_(n,F_Real).b;
  end;
  hence thesis;
end;
