reserve J,J1,K for Element of Segm 13,
  b,b1,b2,c,c1,c2 for Element of SCM+FSA-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;
reserve k for Nat,
  J,K,L for Element of Segm 13,
  O,P,R for Element of Segm 9;
reserve da for Int-Location,
  fa for FinSeq-Location,
  x,y for set;
reserve la,lb for Nat,
  La for Nat,
  i for Instruction of SCM+FSA,
  I for Instruction of SCM,
  l for Nat,
  LA,LB for Nat,
  dA,dB,dC,dD for Element of SCM+FSA-Data-Loc,
  DA,DB,DC for Element of SCM-Data-Loc,
  fA,fB,fC for Element of SCM+FSA-Data*-Loc,
  f,g for FinSeq-Location,
  A,B for Data-Location,
  a,b,c,db for Int-Location;
reserve S for State of SCM,
  s,s1 for State of SCM+FSA;

theorem Th86:
  for I being set holds I is Instruction of SCM+FSA iff
   I = [0,{},{}]
   or (ex a,b st I = a:=b) or (ex a,b st I = AddTo(a,b))
   or (ex a,b st I = SubFrom(a,b)) or
   (ex a,b st I = MultBy(a,b)) or (ex a,b st I = Divide(a,b)) or
   (ex la st I = goto la) or (ex lb,da st I = da=0_goto lb) or
   (ex lb,da st I = da>0_goto lb) or (ex b,a,fa st I = a:=(fa,b)) or
   (ex a,b,fa st I = (fa,a):=b) or
   (ex a,f st I = a:=len f) or ex a,f st I = f:=<0,...,0>a
proof
  let I be set;
  thus I is Instruction of SCM+FSA implies
   I = [0,{},{}]
   or (ex a,b st I = a:=b) or (ex a,b st I = AddTo(a,b))
   or (ex a,b st I = SubFrom(a,b)) or
   (ex a,b st I = MultBy(a,b)) or (ex a,b st I = Divide(a,b)) or
   (ex la st I = goto la) or (ex lb,da st I = da=0_goto lb) or
   (ex lb,da st I = da>0_goto lb) or (ex b,a,fa st I = a:=(fa,b)) or
   (ex a,b,fa st I = (fa,a):=b) or
   (ex a,f st I = a:=len f) or ex a,f st I = f:=<0,...,0>a
  proof
    assume I is Instruction of SCM+FSA;
    then reconsider J = I as Instruction of SCM+FSA;
    set n = InsCode J;
     n = 0 or ... or n = 12 by Th9;
    hence thesis by Th23,Th24,Th25,Th26,Th27,Th28,Th29,Th30,Th31,Th32,Th33,Th34
,Th85;
  end;
  thus thesis by SCMFSA_I:3;
end;
