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
  for s being State of SCM+FSA, s9 being State of SCM
   holds s +* s9  is State of SCM+FSA
 proof
  let s be State of SCM+FSA, s9 being State of SCM;
  reconsider s as SCM+FSA-State by CARD_3:107;
  reconsider s9 as SCM-State by CARD_3:107;
  s +* s9 is SCM+FSA-State by SCMFSA_1:18;
  then s +* s9 is State of SCM+FSA;
  hence thesis;
 end;
