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;
reserve x1,x2,x3,x4 for object;
reserve e,u for object;

theorem
 dom(p^<%e%>) = dom p \/ {card p}
proof
 thus dom(p^<%e%>) = dom(p +* Shift(<%e%>, card p)) by Th74
      .= dom p \/ dom Shift(<%e%>,card p) by FUNCT_4:def 1
      .= dom p \/ {card p} by Th84;
 end;
