reserve P,Q for Instruction-Sequence of SCM+FSA;
reserve m, n for Nat;
reserve f for FinSeq-Location,
  c for Int-Location;
reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;
reserve i,k,m,n for Nat;
reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;

theorem
  for p be preProgram of SCM+FSA,l be Nat,
  ic be Instruction of SCM+FSA st (ex pc be Instruction of SCM+FSA
st pc=p.l & UsedInt*Loc pc=UsedInt*Loc ic)
  holds UsedI*Loc p = UsedI*Loc (p +*(l,ic))
proof
  let p be preProgram of SCM+FSA,l be Nat, ic be Instruction of SCM+FSA;
  given pc be Instruction of SCM+FSA such that
A1:  pc = p.l and
A2: UsedInt*Loc pc = UsedInt*Loc ic;
  { UsedInt*Loc i where i is Instruction of SCM+FSA : i in rng p} =
    { UsedInt*Loc  j where j is Instruction of SCM+FSA : j in rng(p+*(l,ic))}
            from FUNCT_7:sch 7(A2,A1);
 hence thesis;
end;
