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 Th9:
  StepForUp(a,bb,cc,I,p,s).0.a = s.bb
proof
  set aux = 1-stRWNotIn ({a, bb, cc} \/ UsedILoc I);
  set S = s+*(aux, s.cc-s.bb+1)+*(a, s.bb);
  StepWhile>0(aux, I ";" AddTo(a, intloc 0) ";" SubFrom(aux, intloc 0),p,S)
  .0 = S & a in dom (s+*(aux, s.cc-s.bb+1)) by SCMFSA_2:42,SCMFSA_9:def 5;
  hence thesis by FUNCT_7:31;
end;
