reserve m,j,p,q,n,l for Element of NAT;
reserve e1,e2 for ExtReal;

theorem
 for f being Function
 for i,n being Nat st i in dom Shift(f,n)
  ex j being Nat st j in dom f & i = j + n
 proof let f be Function;
  let i,n be Nat;
A1: dom Shift(f,n) = { m+n where m is Nat:m in dom f } by Def12;
  assume i in dom Shift(f,n);
   then ex m being Nat st i = m + n & m in dom f by A1;
  hence ex j being Nat st j in dom f & i = j + n;
 end;
