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 Th11:
  for a be Int_position,i be Integer,I be Program of SCMPDS holds
while<>0(a,i,I). 0=(a,i)<>0_goto 2 & while<>0(a,i,I). 1= goto (card
  I +2) & while<>0(a,i,I). (card I+2)=goto -(card I+2)
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), i3=goto -(card I+2);
  set I4=i1 ';' i2 ';' I;
  set WHL=while<>0(a,i,I);
A1: WHL=i1 ';' i2 ';' (I ';' i3) by SCMPDS_4:11;
  hence WHL. 0=i1 by Th1;
  thus WHL. 1=i2 by A1,Th1;
  card I4=card (i1 ';' i2)+ card I by AFINSQ_1:17
    .=card I +2 by SCMP_GCD:5;
  hence thesis by SCMP_GCD:6;
end;
