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,
      b be Int-Location,a be read-write Int-Location st s.a <= 0
 holds IExec(Times(a,I),p,s).b=(Initialized s).b
proof
  set D= Data-Locations SCM+FSA;
  let s be State of SCM+FSA,
      I be good InitHalting really-closed MacroInstruction of SCM+FSA,
      b be Int-Location,a be read-write Int-Location;
  assume
A1: s.a <= 0;
  set s0 = Initialized s,
      p0 = p;
A2: s0.a=s.a & s0.(intloc 0)=1 by SCMFSA_M:9,37;
  b in Int-Locations by AMI_2:def 16;
  then
A3: b in D by SCMFSA_2:100,XBOOLE_0:def 3;
  DataPart IExec(Times(a,I),p,s) = DataPart IExec(Times(a,I),p0,s0)
   by SCMFSA8C:3
    .= DataPart s0 by A1,A2,Th47;
  hence IExec(Times(a,I),p,s).b= (DataPart s0).b by A3,FUNCT_1:49
    .= s0.b by A3,FUNCT_1:49;
end;
