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;

theorem
  ss1 is subsequence of ss2 & ss2 is subsequence of ss3 implies
  ss1 is subsequence of ss3
proof
  given N1 being increasing sequence of NAT such that
A1: ss1 = ss2*N1;
  given N2 being increasing sequence of NAT such that
A2: ss2 = ss3*N2;
  take N2*N1;
  thus thesis by A1,A2,RELAT_1:36;
end;
