reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem Th16:
  for s being 0-started State of SCMPDS
  for I being parahalting halt-free Program of SCMPDS,k being Nat
   st I c= P & k < LifeSpan(P +* stop I,s)
  holds CurInstr(P,Comput(P,s,k)) <> halt SCMPDS
proof
  let s be 0-started State of SCMPDS;
  let I be parahalting halt-free Program of SCMPDS,k be Nat;
  set PI = P +* stop I, s1= Comput(P, s,k), s2= Comput(PI, s,k);
  assume that
A1: I c= P and
A2: k < LifeSpan(PI,s);
A3: IC s2 in dom I by A2,Th12;
A4: P/.IC s1 = P.IC s1 by PBOOLE:143;
   CurInstr(P,s1)=P.IC s2 by A4,A1,A2,Th13
    .=I.IC s2 by A1,A3,GRFUNC_1:2;
  hence thesis by A3,COMPOS_1:def 27;
end;
