reserve m,n for Nat,
  I for Program of SCM+FSA,
  s,s1,s2 for State of SCM+FSA,
  a for Int-Location,
  f for FinSeq-Location,
  p,p1,p2 for Instruction-Sequence of SCM+FSA;

theorem Th19:
  for I being keepInt0_1 InitHalting really-closed Program of SCM+FSA,
      J being InitHalting really-closed Program of SCM+FSA
 holds IExec(I ";" J,p,s).f = IExec(J,p,IExec(I,p,s)).f
proof
  let I be keepInt0_1 InitHalting really-closed Program of SCM+FSA,
      J be InitHalting really-closed Program of SCM+FSA;
  IExec(I ";" J,p,s) = IncIC(IExec(J,p,IExec(I,p,s)),card I) & not f in dom
Start-At (IC IExec(J,p,IExec(I,p,s)) + card I, SCM+FSA) by Th17,SCMFSA_2:103;
  hence thesis by FUNCT_4:11;
end;
