reserve x for set,
  m,n for Nat,
  a,b for Int_position,
  i,j,k for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem
  for s being State of SCMPDS,I being Program of SCMPDS,a being
  Int_position, i being Integer,n be Nat st s.DataLoc(s.a,i) >= 0
  holds IC IExec(for-up(a,i,n,I),P,Initialize s) = card I + 3
proof
  let s be State of SCMPDS,I be Program of SCMPDS,a be Int_position, i be
  Integer,n be Nat;
  assume
  s.DataLoc(s.a,i) >= 0;
  then IExec(for-up(a,i,n,I),P,Initialize s) =s +* Start-At((card I+3),SCMPDS)
  by Th34;
  hence thesis by FUNCT_4:113;
end;
