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 Th44:
  for i being Instruction of SCM, ii being Instruction of SCM+FSA,
  s being State of SCM, ss being State of SCM+FSA st i = ii & s = ss|SCM-Memory
   holds Exec(ii,ss) = ss +* Exec(i,s)
proof
  let i be Instruction of SCM, ii be Instruction of SCM+FSA, s be State of SCM
  , ss be State of SCM+FSA such that
A1: i = ii and
A2: s = ss|SCM-Memory;
  reconsider SS = ss as SCM+FSA-State by CARD_3:107;
  reconsider II = ii as Element of SCM+FSA-Instr;
  InsCode II <= 8 by A1,AMI_5:5;
  then consider I being Element of SCM-Instr, S being SCM-State such that
A3: I = II & S = SS|SCM-Memory and
A4: SCM+FSA-Exec-Res(II,SS) = SS +* SCM-Exec-Res(I,S) by SCMFSA_1:def 16;
  Exec(i,s) = SCM-Exec-Res(I,S) by A1,A2,A3,AMI_2:def 15;
  hence thesis by A4,SCMFSA_1:def 17;
end;
