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 ::SCMPDS_6:42
  for I being Program of SCMPDS,s being State of SCMPDS, k being Nat
    st I is_halting_on s,P
   & k < LifeSpan(P+*stop I,Initialize s) holds
  CurInstr(P+*stop I,Comput(P +* stop I,Initialize s,k)) <> halt SCMPDS
proof
  let I be Program of SCMPDS,s be State of SCMPDS,k be Nat;
  set ss=Initialize s, PP = P +* stop I,
  m=LifeSpan(PP,ss);
  assume that
A1: I is_halting_on s,P and
A2: k < m;
  assume
A3: CurInstr(PP,Comput(PP,ss,k))=halt SCMPDS;
  PP halts_on ss by A1,SCMPDS_6:def 3;
  hence thesis by A2,A3,EXTPRO_1:def 15;
end;
