reserve n,k,k1,m,m1,n1,n2,l for Nat;
reserve r,r1,r2,p,p1,g,g1,g2,s,s1,s2,t for Real;
reserve seq,seq1,seq2 for Real_Sequence;
reserve Nseq for increasing sequence of NAT;
reserve x for set;
reserve X,Y for Subset of REAL;

theorem Th3:
  for r ex n st r<n
proof
  let r;
  for r st r in NAT holds r+1 in NAT by AXIOMS:2;
  then consider p such that
A1: p in NAT and
A2: r<p by Th2, NUMBERS:19;
  consider n1 such that
A3: n1=p by A1;
  take n1;
  thus thesis by A2,A3;
end;
