reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem Th9:
  for s1,s2 being 0-started State of SCM+FSA,
      I being really-closed Program of SCM+FSA
   st I c= P1 & I c= P2 & DataPart s1 = DataPart s2
  for i being Nat
  holds IC Comput(P1, s1,i) = IC Comput(P2, s2,i) &
  CurInstr(P1,Comput(P1,s1,i)) = CurInstr(P2,Comput(P2,s2,i)) &
  DataPart Comput(P1, s1,i) = DataPart Comput(P2,s2,i)
proof
  let s1,s2 be 0-started State of SCM+FSA;
  let J be really-closed Program of SCM+FSA;
  assume that
A1: J c= P1 and
A2: J c= P2 and
A3: DataPart s1 = DataPart s2;
A4: Start-At(0,SCM+FSA) c= s2 by MEMSTR_0:29;
A5: Reloc(J,0) = J;
  let i be Nat;
A6: IC SCM+FSA in dom Start-At(0,SCM+FSA) by MEMSTR_0:15;
A7: IC Comput(P1, s1,i) + 0 = IC Comput(P1, s1,i);
A8: IC s2 = IC (Initialize s2) by A4,FUNCT_4:98
    .= IC Start-At(0,SCM+FSA) by A6,FUNCT_4:13
    .=  0 by FUNCOP_1:72;
  IncAddr(CurInstr(P1,Comput(P1,s1,i)),0)
   = CurInstr(P1,Comput(P1,s1,i)) by COMPOS_0:3;
  hence thesis by A3,A7,A8,Th8,A1,A2,A5;
end;
