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 Th47:
  s1 = s +* S & A = a implies S.A = s1.a
proof
  assume that
A1: s1 = s +* S and
A2: A = a;
 dom S = SCM-Memory by PARTFUN1:def 2;
  hence s1.a = S.A by A1,A2,FUNCT_4:13;
end;
