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;

theorem Th31:
  for ins being Instruction of SCM+FSA st InsCode ins = 9 holds ex
  a,b,fa st ins = b:=(fa,a)
proof
  let ins be Instruction of SCM+FSA such that
A1: InsCode ins = 9;
A2: now
    assume ins in { [K,{},<*dC,fB*>] : K in {11,12} };
    then consider K,dC,fB such that
A3: ins = [K,{},<*dC,fB*>] and
A4: K in {11,12};
    K = 11 or K = 12 by A4,TARSKI:def 2;
    hence contradiction by A1,A3;
  end;
  ins in SCM-Instr \/ { [L,{},<*dB,fA,dA*>] where L is Element of Segm 13,
    dA,dB is Element of SCM+FSA-Data-Loc,fA is Element of SCM+FSA-Data*-Loc
    : L in {9,10} } or
   ins in { [K,{},<*dC,fB*>] : K in {11,12} }
    by XBOOLE_0:def 3;
  then ins in SCM-Instr or ins in { [L,{},<*dB,fA,dA*>] : L in {9,10} } by A2,
XBOOLE_0:def 3;
  then consider L be Element of Segm 13,
    dA,dB be Element of SCM+FSA-Data-Loc,fA be Element of SCM+FSA-Data*-Loc
    such that
A5: ins = [L,{},<*dB,fA,dA*>] and
  L in {9,10} by A1,AMI_5:5;
  reconsider f=fA as FinSeq-Location by Def3;
  reconsider c = dB, b = dA as Int-Location by AMI_2:def 16;
  take b,c,f;
  thus thesis by A1,A5;
end;
