reserve m for Nat;
reserve P for Instruction-Sequence of SCM+FSA;

theorem Th2:
  for P being preProgram of SCM+FSA, n being Element of NAT, a
being Int-Location st P does not destroy a
  holds Reloc(P,n) does not destroy a
proof
  let I be preProgram of SCM+FSA;
  let n be Element of NAT;
  let a be Int-Location;
A1: dom IncAddr(I,n) = dom I by COMPOS_1:def 21;
A2: dom Shift(IncAddr(I,n),n) = { m+n where m is Nat: m in dom IncAddr(I,n) }
    by VALUED_1:def 12;
  assume
A3: I does not destroy a;
  now
    let i be Instruction of SCM+FSA;
    assume i in rng Reloc(I,n);
    then consider x being object such that
A4: x in dom Shift(IncAddr(I,n),n) and
A5: i = Shift(IncAddr(I,n),n).x by FUNCT_1:def 3;
    consider m being Nat such that
A6: x = m + n and
A7: m in dom IncAddr(I,n) by A2,A4;
A8: I. m in rng I by A1,A7,FUNCT_1:def 3;
    rng I c= the InstructionsF of SCM+FSA by RELAT_1:def 19;
    then reconsider ii = I. m as Instruction of SCM+FSA by A8;
A9: ii does not destroy a by A3,A8,SCMFSA7B:def 4;
    i = IncAddr(I,n). m by A5,A6,A7,VALUED_1:def 12
      .= IncAddr(I/.m,n) by A1,A7,COMPOS_1:def 21
      .= IncAddr(ii,n) by A1,A7,PARTFUN1:def 6;
    hence i does not destroy a by A9,Th1;
  end;
  hence thesis by SCMFSA7B:def 4;
end;
