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
  seq is non-decreasing implies inferior_realsequence seq = seq
proof
  assume seq is non-decreasing;
  then for n being Element of NAT holds
   (inferior_realsequence seq).n = seq.n by Lm2;
  hence thesis by FUNCT_2:63;
end;
