reserve x,y for object,X for set,
  f for Function,
  R,S for Relation;
reserve e1,e2 for ExtReal;
reserve s,s1,s2,s3 for sequence of X;
reserve XX for non empty set,
        ss,ss1,ss2,ss3 for sequence of XX;
reserve X,Y for non empty set,
  Z for set;
reserve s,s1 for sequence of X,
  h,h1 for PartFunc of X,Y,
  h2 for PartFunc of Y ,Z,
  x for Element of X,
  N for increasing sequence of NAT;
reserve i,j for Nat;

theorem
  s is constant & s1 is subsequence of s implies s = s1
proof
  assume that
A1: s is constant and
A2: s1 is subsequence of s;
  let n be Element of NAT;
  consider N such that
A3: s1=s*N by A2,Def13;
  thus s1.n=s.(N.n) by A3,FUNCT_2:15
    .=s.n by A1,Th23;
end;
