reserve a,b,c,d for Ordinal;
reserve l for non empty limit_ordinal Ordinal;
reserve u for Element of l;
reserve A for non empty Ordinal;
reserve e for Element of A;
reserve X,Y,x,y,z for set;
reserve n,m for Nat;

theorem Th9:
  for f1,f2 being Sequence holds f1 c= f1^f2
  proof
    let f1,f2 be Sequence;
    dom(f1^f2) = (dom f1)+^dom f2 by ORDINAL4:def 1; then
A1: dom f1 c= dom(f1^f2) by ORDINAL3:24;
    for x being object st x in dom f1 holds f1.x = (f1^f2).x
       by ORDINAL4:def 1;
    hence f1 c= f1^f2 by A1,GRFUNC_1:2;
  end;
