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

theorem
  for s being 0-started State of SCMPDS,I being Program of SCMPDS, a,b being
Int_position , i being Integer st s.DataLoc(s.a,i) <= 0
 holds IExec(while>0(a,i,I),P,s).b = s.b
proof
  let s be 0-started State of SCMPDS,I be Program of SCMPDS,
      a,b be Int_position, i be Integer;
  assume s.DataLoc(s.a,i) <= 0;
  then
A1: IExec(while>0(a,i,I),P,s) = s +* Start-At((card I+2),SCMPDS)
 by Th19;
  not b in dom Start-At((card I+2),SCMPDS) by SCMPDS_4:18;
  hence thesis by A1,FUNCT_4:11;
end;
