reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;
reserve i for Nat;
reserve m for Nat,
        D for non empty set;
reserve l for Nat;
reserve M for Nat;
reserve m,n for Nat;

theorem Th77:
  Shift(p,n) c= Shift(p^q,n)
 proof
    p^q = p +* Shift(q, card p) by Th74;
    then
A1:   Shift(p^q,n) = Shift(p,n) +* Shift(Shift(q,card p),n) by VALUED_1:23;
    Shift(Shift(q,card p),n) = Shift(q,n+card p) by VALUED_1:21;
    then dom Shift(p,n) misses dom Shift(Shift(q,card p),n) by Th76;
   hence Shift(p,n) c=  Shift(p^q,n) by A1,FUNCT_4:32;
 end;
