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;
reserve P,P1,P2,Q for Instruction-Sequence of SCM+FSA;

theorem
  for s be State of SCM+FSA,
     I be good InitHalting really-closed MacroInstruction of
SCM+FSA, a be read-write Int-Location st s.a > 0 & while>0(a,I) is InitHalting
holds DataPart IExec(while>0(a,I),P,s) =
 DataPart IExec(while>0(a,I),P,IExec(I,P,s)) by Lm8;
