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

theorem Th27:
  for I,J being MacroInstruction of SCM+FSA,a being Int-Location holds if>0
  (a,I,J). (card J + 2) = goto  (card I + card J + 3)
proof
  let I,J be MacroInstruction of SCM+FSA;
  let a be Int-Location;
  set JJ = a >0_goto  (card J + 3) ";" J;
  set J3 = a >0_goto  (card J + 3) ";" J ";" Goto  (card I + 1);
A1: card JJ = card Macro (a >0_goto  (card J + 3)) + card J by SCMFSA6A:21
    .= 2 + card J by COMPOS_1:56;
  then card J + 2 -' card JJ = 0 by XREAL_1:232;
  then
A2: goto  (card I + 1) = (Goto  (card I + 1)). (card J + 2
  -' card JJ);
  card Goto  (card I + 1) = 1 by SCMFSA8A:15;
  then card J + 2 < card JJ + card Goto  (card I + 1) by A1,NAT_1:13;
  then
A3: J3. (card J + 2) = IncAddr(goto  (card I + 1),card JJ) by A1,A2,Th2
    .= goto  (card I + 1 + (card J + 2)) by A1,SCMFSA_4:1
    .= goto  (card I + card J + (1 + 2));
  card Goto  (card I + 1) = 1 by SCMFSA8A:15;
  then card J3 = card J + 2 + 1 by A1,SCMFSA6A:21
    .= card J + (2 + 1);
  then card J3 = card J + 2 + 1;
  then card J + 2 < card J3 by NAT_1:13;
  then
A4:  (card J + 2) in dom J3 by AFINSQ_1:66;
  then (J3 ";" (I ";" Stop SCM+FSA)). (card J + 2) = (Directed J3).
   (card J + 2) by SCMFSA8A:14
    .= goto  (card I + card J + 3) by A3,A4,SCMFSA8A:16;
  hence thesis by SCMFSA6A:25;
end;
