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
  for s being 0-started State of SCM+FSA,
      I being good InitHalting really-closed MacroInstruction of
SCM+FSA, a being read-write Int-Location
   st I does not destroy a & s.intloc 0 = 1
 holds Times(a,I) is_halting_on s,p
proof
  let s be 0-started State of SCM+FSA;
  let I be good InitHalting really-closed MacroInstruction of SCM+FSA;
  let a be read-write Int-Location;
  assume
A1: I does not destroy a;
  assume
A2: s.intloc 0 = 1;
   ProperTimesBody a, I, s, p
    proof let k be Nat such that
    k < s.a;
     thus I is_halting_on StepTimes(a,I,p,s).k, p+*Times(a,I) by A1,A2,Lm3;
    end;
  hence thesis by A1,A2,SCMFSA9A:55;
end;
