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 Th60:
  seq is bounded_above implies (superior_realsequence seq).n = - (
  inferior_realsequence(-seq)).n
proof
  assume
A1: seq is bounded_above;
  (superior_realsequence seq).n = upper_bound (seq ^\n) by Th37
    .= - lower_bound -(seq ^\n) by A1,Th13,SEQM_3:27
    .= - lower_bound ((-seq) ^\n) by SEQM_3:16;
  hence thesis by Th36;
end;
