reserve p,p1,p2,h for Instruction-Sequence of SCM+FSA;
reserve k, l, n for Nat,
  j for Integer,
  i,i1 for Instruction of SCM+FSA;
reserve s, s1, s2 for State of SCM+FSA,
  a for read-write Int-Location,
  b for Int-Location,
  I, J for MacroInstruction of SCM+FSA,
  Ig for good MacroInstruction of SCM+FSA,
  i, j, k, m, n for Nat;

theorem  :: ifUsedF:
  UsedI*Loc if>0(b, I, J) = UsedI*Loc I \/ UsedI*Loc J
proof
  set I5 = Stop SCM+FSA;
  set a = b;
  set I1 = a >0_goto  (card J + 3);
  set I3 = Goto  (card I + 1);
  thus UsedI*Loc if>0(a, I, J) = UsedI*Loc (I1 ";" J ";" I3 ";" I ";" I5)
    .= (UsedI*Loc (I1 ";" J ";" I3 ";" I)) \/ {} by Th4,SF_MASTR:43
    .= (UsedI*Loc (I1 ";" J ";" I3)) \/ UsedI*Loc I by SF_MASTR:43
    .= (UsedI*Loc (I1 ";" J)) \/ UsedI*Loc I3 \/ UsedI*Loc I by SF_MASTR:43
    .= (UsedI*Loc (I1 ";" J)) \/ {} \/ UsedI*Loc I by Th6
    .= UsedInt*Loc I1 \/ UsedI*Loc J \/ UsedI*Loc I by SF_MASTR:45
    .= {} \/ UsedI*Loc J \/ UsedI*Loc I by SF_MASTR:32
    .= UsedI*Loc I \/ UsedI*Loc J;
end;
