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 Th13:
  StepForUp(a,bb,cc,I,p,s).0.f = s.f
proof
  set aux = 1-stRWNotIn ({a, bb, cc} \/ UsedILoc I);
  set S = s+*(aux, s.cc-s.bb+1)+*(a, s.bb);
  S.f = (s+*(aux, s.cc-s.bb+1)).f by FUNCT_7:32,SCMFSA_2:58
    .= s.f by FUNCT_7:32,SCMFSA_2:58;
  hence thesis by SCMFSA_9:def 5;
end;
