reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem Th24:
  for I,J being MacroInstruction of SCM+FSA,a being Int-Location
   holds if=0
  (a,I,J). (card I + card J + 3) = halt SCM+FSA
proof
  let I,J be MacroInstruction of SCM+FSA;
  let a be Int-Location;
  set II = a =0_goto  (card J + 3) ";" J ";" Goto  (card I + 1)
  ";" I;
A1: card II = card (Macro (a =0_goto  (card J + 3)) ";" J ";" Goto
   (card I + 1)) + card I by SCMFSA6A:21
    .= card (Macro (a =0_goto  (card J + 3)) ";" J) + card Goto
  (card I + 1) + card I by SCMFSA6A:21
    .= card (Macro (a =0_goto  (card J + 3)) ";" J) + 1 + card I by SCMFSA8A:15
    .= card Macro (a =0_goto  (card J + 3)) + card J + 1 + card I by
SCMFSA6A:21
    .= 2 + card J + 1 + card I by COMPOS_1:56
    .= card I + card J + 3;
  then
A2: card I + card J + 3 -' card II = 0 by XREAL_1:232;
A3: (Stop SCM+FSA).0 = halt SCM+FSA;
  card Stop SCM+FSA = 1 by AFINSQ_1:34;
  then card I + card J + 3 < card II + card Stop SCM+FSA by A1,NAT_1:13;
  hence
  if=0(a,I,J). (card I + card J + 3) = IncAddr(halt SCM+FSA,card II
  ) by A1,A2,Th2,A3
    .= halt SCM+FSA by COMPOS_0:4;
end;
