reserve n,k,k1,m,m1,n1,n2,l for Nat;
reserve r,r1,r2,p,p1,g,g1,g2,s,s1,s2,t for Real;
reserve seq,seq1,seq2 for Real_Sequence;
reserve Nseq for increasing sequence of NAT;
reserve x for set;
reserve X,Y for Subset of REAL;

theorem Th44:
  for X being non empty real-membered set st (for s st s in X holds s >=
r) & for t st for s st s in X holds s >= t holds r >= t holds r = lower_bound X
  by Lm1;
