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 Th48:
  seq is bounded_below implies (inferior_realsequence seq).n <= (
  inferior_realsequence seq).(n+1)
proof
A1: min((inferior_realsequence seq).(n+1),seq.n) <= (inferior_realsequence
  seq).(n+1) by XXREAL_0:17;
  assume seq is bounded_below;
  hence thesis by A1,Th46;
end;
