reserve x,a for Int_position,
  s for State of SCMPDS;

theorem Th4:
  for a be Int_position,i be Integer,I be Program of SCMPDS holds
  card while<0(a,i,I)= card I +2
proof
  let a be Int_position,i be Integer, I be Program of SCMPDS;
  set i1=(a,i)>=0_goto (card I +2);
  set I4=i1 ';' I;
  thus card while<0(a,i,I)=card I4+1 by SCMP_GCD:4
    .=card I +1 +1 by SCMPDS_6:6
    .=card I + 2;
end;
