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 Th8:
  for a be Int_position,i be Integer,I be Program of SCMPDS holds
  card while<>0(a,i,I)= card I +3
proof
  let a be Int_position,i be Integer, I be Program of SCMPDS;
  set i1=(a,i)<>0_goto 2, i2=goto (card I+2);
  set I4=i1 ';' i2 ';' I;
  thus card while<>0(a,i,I) =card I4+1 by SCMP_GCD:4
    .=card (i1 ';' i2)+ card I+1 by AFINSQ_1:17
    .=2+card I +1 by SCMP_GCD:5
    .=card I + 3;
end;
