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 Th10:
  lower_bound {r} = upper_bound {r}
proof
  lower_bound {r}=r by XXREAL_2:13;
  hence thesis by XXREAL_2:11;
end;
