reserve m for Nat;
reserve P for (the InstructionsF of SCM+FSA)-valued ManySortedSet of NAT;

theorem
  for a being Int-Location, k being Integer holds a:=k = aSeq(a,k)
  ^ Stop SCM+FSA
proof
  let a be Int-Location, k be Integer;
  per cases;
  suppose
    k > 0;
    then
    ex k1 being Nat st k1 + 1 = k & a:=k = <% a:=intloc 0
    %> ^ (k1-->AddTo(a,intloc 0)) ^ Stop SCM+FSA by Def1;
    hence thesis by Def2;
  end;
  suppose
A1: k <= 0;
    then
    ex k1 being Nat st k1 + k = 1 & a:=k =  <% a:=intloc 0
    %> ^ (k1-->SubFrom(a,intloc 0)) ^ Stop SCM+FSA by Def1;
    hence thesis by A1,Def2;
  end;
end;
