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

theorem Th22:
  for T being TuringStr,t be Tape of T, s be Element of NAT, f be
FinSequence of NAT st len f >=1 & t storeData <*s*>^f holds t is_1_between s,s+
  f/.1+2
proof
  let T be TuringStr,t be Tape of T,s be Element of NAT, f be FinSequence of
  NAT;
  set g=<*s*>^f;
  assume that
A1: len f >=1 and
A2: t storeData g;
  len <*s*>=1 by FINSEQ_1:39;
  then len g=1+len f by FINSEQ_1:22;
  then len g >= 1+1 by A1,XREAL_1:7;
  then
A3: 1 < len g by XXREAL_0:2;
  Sum Prefix(g,1)+2*(1-1)=s & Sum Prefix(g,1+1)+2*1=s+f/.1+2 by A1,Th20;
  hence thesis by A2,A3;
end;
