reserve m,j,p,q,n,l for Element of NAT;
reserve e1,e2 for ExtReal;
reserve i for Nat,
        k,k1,k2,j1 for Element of NAT,
        x,x1,x2,y for set;
reserve p1,p2 for FinSequence;

theorem
 for F being total NAT-defined Function, p be NAT-defined Function,
     n be Element of NAT st Shift(p,n) c= F
 for i being Element of NAT st i in dom p holds F.(n+i) = p.i
 proof
  let F be total NAT-defined Function, p be NAT-defined Function,
     n be Element of NAT such that
A1: Shift(p,n) c= F;
  let i be Element of NAT;
  assume
A2: i in dom p;
   then n+i in dom Shift(p,n) by Th24;
  hence F.(n+i) = Shift(p,n).(n+i) by A1,GRFUNC_1:2
      .= p.i by A2,Def12;
 end;
