reserve s for State of SCM+FSA,
  a, c for read-write Int-Location,
  aa, bb, cc,
  dd, x for Int-Location,
  f for FinSeq-Location,
  I, J for MacroInstruction of SCM+FSA,
  Ig for good MacroInstruction of SCM+FSA,
  i, k for Nat,
  p for Instruction-Sequence of SCM+FSA;

theorem Th6:
 for I,J being MacroInstruction of SCM+FSA holds
  UsedILoc if>0(aa, bb, I, J) = {aa, bb} \/ (UsedILoc I) \/ UsedILoc J
proof let I,J be MacroInstruction of SCM+FSA;
  set a = aa;
  thus UsedILoc if>0(a, bb, I, J) = UsedILoc (SubFrom(a,bb) ";" if>0(a,I,J
  )) by SCMFSA8B:def 5
    .= (UsedIntLoc SubFrom(a,bb)) \/ UsedILoc if>0(a,I,J) by SF_MASTR:29
    .= {a,bb} \/ UsedILoc if>0(a,I,J) by SF_MASTR:14
    .= {a,bb} \/ ({a} \/ UsedILoc I \/ UsedILoc J) by SCMFSA9A:9
    .= {a,bb} \/ ({a} \/ (UsedILoc I \/ UsedILoc J)) by XBOOLE_1:4
    .= {a,bb} \/ {a} \/ ((UsedILoc I \/ UsedILoc J)) by XBOOLE_1:4
    .= {a, bb} \/ (UsedILoc I \/ UsedILoc J) by ZFMISC_1:9
    .= {a, bb} \/ UsedILoc I \/ UsedILoc J by XBOOLE_1:4;
end;
