reserve m,n for Nat,
  I for Program of SCM+FSA,
  s,s1,s2 for State of SCM+FSA,
  a for Int-Location,
  f for FinSeq-Location,
  p,p1,p2 for Instruction-Sequence of SCM+FSA;

theorem Th1:
  Macro halt SCM+FSA is InitHalting
proof
  let s be State of SCM+FSA;
  set m = Macro halt SCM+FSA;
  set m1 = m;
  assume
A1: iS c= s;
  let p be Instruction-Sequence of SCM+FSA;
  assume
A2: m c= p;
A3: IC SCM+FSA in dom iS by MEMSTR_0:48;
  take 0;
     IC Comput(p,s,0) in NAT;
    hence IC Comput(p,s,0) in dom p by PARTFUN1:def 2;
A4: m. 0 = halt SCM+FSA by COMPOS_1:58;
  dom m = { 0, 1} by COMPOS_1:61;
  then
A5:  0 in dom m by TARSKI:def 2;
A6:  p/.IC s = p.IC s by PBOOLE:143;
  CurInstr(p,Comput(p,s,0))
   = CurInstr(p,s)
    .= p.0 by Lm1,A1,A6,A3,GRFUNC_1:2
    .= halt SCM+FSA by A4,A2,A5,GRFUNC_1:2;
    hence thesis;
end;
