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 Th24:
  |.w.| = 0 implies w = 0.TOP-REAL N
proof
  reconsider s = w as Element of REAL N by EUCLID:22;
  assume |.w.| = 0;
  then s = 0*N by EUCLID:8
    .= 0.TOP-REAL N by EUCLID:70;
  hence thesis;
end;
