reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;
reserve aa,bb for Int-Location;
reserve s for State of SCM+FSA,
  a for Int-Location,
  I for Program of SCM+FSA,
  p for Instruction-Sequence of SCM+FSA;

theorem
 for I being MacroInstruction of SCM+FSA holds
  I does not destroy aa implies
  if=0(bb, I ';' goto 0) does not destroy aa
 proof let I be MacroInstruction of SCM+FSA;
  set i = bb =0_goto 3, Mi=Macro i;
  set IG = I ';' goto 0;
A1: Stop SCM+FSA does not destroy aa by Th47;
  assume I does not destroy aa;
  then
A2: I ';' goto  0 does not destroy aa by Lm2;
A3: Goto  (card IG + 1) does not destroy aa by Th48;
  i does not destroy aa;
  then i ";" Goto  (card IG + 1) does not destroy aa by A3,Th44;
  then i ";" Goto(card IG + 1) ";" IG does not destroy aa by A2,Th43;
  hence thesis by A1,Th43;
 end;
