reserve N for Nat;
reserve n,m,n1,n2 for Nat;
reserve q,r,r1,r2 for Real;
reserve x,y for set;
reserve w,w1,w2,g,g1,g2 for Point of TOP-REAL N;
reserve seq,seq1,seq2,seq3,seq9 for Real_Sequence of N;

theorem
  seq is non-zero implies -seq is non-zero
proof
  assume seq is non-zero;
  then (-1)*seq is non-zero by Th21;
  hence thesis by Th11;
end;
