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
  w1 <> w2 implies |.w1 - w2.| > 0
proof
  reconsider s1 = w1, s2 = w2 as Element of REAL N by EUCLID:22;
  s1 - s2 = w1 - w2;
  hence thesis by EUCLID:17;
end;
