reserve m,n for Element of NAT,
  i,j for Instruction of SCMPDS,
  I for Program
  of SCMPDS,
  a for Int_position;
reserve Q,U,P for Instruction-Sequence of SCMPDS;

theorem Th9:
  for a be Int_position,i be Integer,m be Element of NAT,I be
  Program of SCMPDS holds m < card I+3 iff  m in dom while<>0(a,i,I)
proof
  let a be Int_position,i be Integer,m be Element of NAT, I be Program of
  SCMPDS;
  card while<>0(a,i,I)=card I + 3 by Th8;
  hence thesis by AFINSQ_1:66;
end;
