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 Th10:
  for a be Int_position,i be Integer,I be Program of SCMPDS holds
   0 in dom while<>0(a,i,I) &  1 in dom while<>0(a,i,I)
proof
  let a be Int_position,i be Integer,I be Program of SCMPDS;
  3 <= card I+3 by NAT_1:11;
  then 0 < card I+3 & 1 < card I+3 by XXREAL_0:2;
  hence thesis by Th9;
end;
