reserve x,a for Int_position,
  s for State of SCMPDS;
reserve P,Q for Instruction-Sequence of SCMPDS;

theorem Th17:
  for a be Int_position,i be Integer,I be Program of SCMPDS holds
   while>0(a,i,I). 0=(a,i)<=0_goto (card I +2) &
   while>0(a,i,I). (card I+1)=goto -(card I+1)
proof
  let a be Int_position,i be Integer,I be Program of SCMPDS;
  set i1=(a,i)<=0_goto (card I +2), i2=goto -(card I+1);
  set I4=i1 ';' I;
  set J5=I ';' i2;
  set WHL=while>0(a,i,I);
  WHL=i1 ';' J5 by SCMPDS_4:15;
  hence WHL. 0=i1 by SCMPDS_6:7;
  card I4=card I+1 by SCMPDS_6:6;
  hence thesis by SCMP_GCD:6;
end;
