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

theorem
 for I being Program of SCM+FSA, a being Int-Location,
     k being Nat, i being Instruction of SCM+FSA
   st I does not destroy a & i does not destroy a
 holds I +*(k,i) does not destroy a
proof
 let I be Program of SCM+FSA, a be Int-Location,
     k be Nat, i be Instruction of SCM+FSA such that
A1: I does not destroy a and
A2: i does not destroy a;
 let j be Instruction of SCM+FSA such that
A3: j in rng(I +*(k,i));
  rng(I+*(k,i)) c= rng I \/ {i} by FUNCT_7:100;
 then j in rng I \/ {i} by A3;
 then per cases by XBOOLE_0:def 3;
 suppose j in rng I;
  hence thesis by A1,SCMFSA7B:def 4;
 end;
 suppose j in {i};
  hence j does not destroy a by A2,TARSKI:def 1;
 end;
end;
