reserve n,n1,m,k for Nat;
reserve x,y for set;
reserve s,g,g1,g2,r,p,p2,q,t for Real;
reserve s1,s2,s3 for Real_Sequence;
reserve Nseq for increasing sequence of NAT;
reserve X for Subset of REAL;

theorem
  for N being Neighbourhood of r holds r in N
proof
  let N be Neighbourhood of r;
  ( ex g st 0<g & N = ].r-g,r+g.[)& |.r-r.| = 0 by Def6,ABSVALUE:2;
  hence thesis by Th1;
end;
