reserve n,i,j,k for Nat;
reserve T for TuringStr,
  s for All-State of T;

theorem Th48:
  for f being FinSequence of NAT,tm1,tm2 be TuringStr,t1 be Tape
  of tm1, t2 be Tape of tm2 st t1=t2 & t1 storeData f holds t2 storeData f
proof
  let f be FinSequence of NAT,tm1,tm2 be TuringStr,t1 be Tape of tm1, t2 be
  Tape of tm2;
  assume that
A1: t1=t2 and
A2: t1 storeData f;
  now
    let i be Nat;
    set m=Sum Prefix(f,i)+2*(i-1), n=Sum Prefix(f,i+1)+2*i;
    assume 1 <= i & i < len f;
    then
A3: t1 is_1_between m,n by A2;
    then
A4: for k be Integer st m < k & k < n holds t1.k=1;
    t1.m=0 & t1.n=0 by A3;
    hence t2 is_1_between m,n by A1,A4;
  end;
  hence thesis;
end;
