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

theorem Th23:
  for T being TuringStr,t be Tape of T, s be Element of NAT, f be
FinSequence of NAT st len f >=3 & t storeData <*s*>^f holds t is_1_between s,s+
f/.1+2 & t is_1_between s+f/.1+2, s+f/.1+f/.2+4 & t is_1_between s+f/.1+f/.2+4,
  s+f/.1+f/.2+f/.3+6
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 >=3 and
A2: t storeData g;
  thus t is_1_between s,s+f/.1+2 by A1,A2,Th22,XXREAL_0:2;
  len <*s*>=1 by FINSEQ_1:39;
  then len g=1+len f by FINSEQ_1:22;
  then
A3: len g >= 3+1 by A1,XREAL_1:7;
  then
A4: 2 < len g by XXREAL_0:2;
  Sum Prefix(g,2)+2*(2-1)=s+f/.1+2 & Sum Prefix(g,2+1)+2*2=s+f/.1+f/.2+4
  by A1,Th21;
  hence t is_1_between s+f/.1+2,s+f/.1+f/.2+4 by A2,A4;
A5: 3 < len g by A3,XXREAL_0:2;
  Sum Prefix(g,3)+2*(3-1)=s+f/.1+f/.2+4 & Sum Prefix(g,3+1)+2*3=s+f/.1+f/.
  2+f /.3+6 by A1,Th21;
  hence thesis by A2,A5;
end;
