theorem
  rng s c= dom h & s1 is subsequence of s implies h/*s1 is subsequence of h/*s
proof
  assume that
A1: rng s c= dom h and
A2: s1 is subsequence of s;
  consider N such that
A3: s1=s*N by A2,Def13;
  take N;
  thus thesis by A1,A3,FUNCT_2:110;
end;
