reserve n,m,k,k1,k2 for Nat;
reserve X for non empty Subset of ExtREAL;
reserve Y for non empty Subset of REAL;
reserve seq for ExtREAL_sequence;
reserve e1,e2 for ExtReal;
reserve rseq for Real_Sequence;

theorem Th23:
  inf seq <= seq.n & seq.n <= sup seq
proof
A1: inf rng seq is LowerBound of rng seq by XXREAL_2:def 4;
A2: sup rng seq is UpperBound of rng seq by XXREAL_2:def 3;
  n in NAT by ORDINAL1:def 12;
  then seq.n in rng seq by FUNCT_2:4;
  hence thesis by A1,A2,XXREAL_2:def 1,def 2;
end;
