reserve m, n for Nat,
  x for set,
  i for Instruction of SCM+FSA,
  I for Program of SCM+FSA,
  a for Int-Location,
  f for FinSeq-Location,
  l, l1 for Nat,
  s,s1,s2 for State of SCM+FSA,
  P,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem
  IC s = l & P.l = goto l implies not P halts_on s
proof
  assume that
A1: IC s = l and
A2: P.l = goto l;
A3:  P/.IC s = P.IC s by PBOOLE:143;
  defpred X[Nat] means  Comput(P,s,$1) = s;
A4: for m st X[m] holds X[m+1]
  proof
    let m;
A5: for f being FinSeq-Location holds Exec(goto l,s).f = s.f by SCMFSA_2:69;
A6: IC Exec(goto l,s) = IC s & for a being Int-Location holds Exec(goto l,
    s).a = s.a by A1,SCMFSA_2:69;
    assume
A7:    Comput(P,s,m) =  s;
    thus  Comput(P,s,m+1)
      =  Following(P,s) by A7,EXTPRO_1:3
     .=  s by A1,A2,A6,A5,A3,SCMFSA_2:104;
  end;
  let mm be Nat;
   reconsider m=mm as Element of NAT by ORDINAL1:def 12;
A8: X[0];
 for m holds X[m] from NAT_1:sch 2(A8,A4);
 then
A9: X[m];
 assume IC Comput(P,s,mm) in dom P;
 thus CurInstr(P, Comput(P,s,mm)) <> halt SCM+FSA by A1,A2,A9,PBOOLE:143;

end;
