reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;
reserve i,j,k,n for Nat;
reserve P,P1,P2,Q for Instruction-Sequence of SCM+FSA;

theorem Th16:
  for s be State of SCM+FSA,
      I be good InitHalting really-closed MacroInstruction of
SCM+FSA, f be FinSeq-Location,a be read-write Int-Location st s.a > 0 & while>0
(a,I) is InitHalting
 holds IExec(while>0(a,I),P,s).f =IExec(while>0(a,I),P,IExec(I,P,
  s)).f
proof
  let s be State of SCM+FSA,
      I be good InitHalting really-closed MacroInstruction of SCM+FSA, f be
  FinSeq-Location,a be read-write Int-Location;
  set D = Data-Locations SCM+FSA;
  assume that
A1: s.a > 0 and
A2: while>0(a,I) is InitHalting;
  f in FinSeq-Locations by SCMFSA_2:def 5;
  then
A3: f in D by SCMFSA_2:100,XBOOLE_0:def 3;
  then IExec(while>0(a,I),P,s).f =(DataPart IExec(while>0(a,I),P,s)).f by
FUNCT_1:49
    .=(DataPart IExec(while>0(a,I),P,IExec(I,P,s))).f by A1,A2,SCM_HALT:75;
  hence thesis by A3,FUNCT_1:49;
end;
