reserve n,m,k,k1,k2 for Nat;
reserve r,r1,r2,s,t,p for Real;
reserve seq,seq1,seq2 for Real_Sequence;
reserve x,y for set;

theorem Th49:
  seq is bounded_above implies (superior_realsequence seq).(n+1)
  <= (superior_realsequence seq).n
proof
A1: (superior_realsequence seq).(n+1) <= max((superior_realsequence seq).(n+
  1),seq.n) by XXREAL_0:25;
  assume seq is bounded_above;
  hence thesis by A1,Th47;
end;
