reserve m,n for Nat,
  a for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1 for Integer,
  loc for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

theorem
  for s being State of SCMPDS,I being Program of SCMPDS,a,b being
Int_position, k1 being Integer st s.DataLoc(s.a,k1) > 0
 holds IExec(if<=0(a,k1,I),P,Initialize s).b = s.b
proof
  let s be State of SCMPDS,I be Program of SCMPDS,a,b be Int_position, k1 be
  Integer;
  assume
  s.DataLoc(s.a,k1) > 0;
  then
A1: IExec(if<=0(a,k1,I),P,Initialize s) = s +* Start-At((card I+2),SCMPDS)
 by Th82;
  not b in dom Start-At((card I+2),SCMPDS) by SCMPDS_4:18;
  hence thesis by A1,FUNCT_4:11;
end;
