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

theorem Th16:
  for T being TuringStr, t be Tape of T, s,n be Element of NAT st
  t is_1_between s,s+n+2 holds t storeData <*s,n*>
proof
  let T be TuringStr,t be Tape of T,s,n be Element of NAT;
  set f=<*s,n*>;
  assume
A1: t is_1_between s,s+n+2;
A2: Sum Prefix(f,1+1)+2*1=s+n+2 by Th4;
  now
    let i be Nat;
    assume that
A3: 1 <= i and
A4: i < len f;
    len f=2 by FINSEQ_1:44;
    then i+1 <= 1+1 by A4,INT_1:7;
    then i <= 1 by XREAL_1:6;
    then i=1 by A3,XXREAL_0:1;
    hence
    t is_1_between Sum Prefix(f,i)+2*(i-1),Sum Prefix(f,i+1)+2*i by A1,A2,Th4;
  end;
  hence thesis;
end;
