
theorem
  for m,k be Nat, r be Tuple of (m+2),k-SD st k >= 2 holds SDDec(M0(r))
<= SDDec(r) & SDDec(r) <= SDDec(Mmax(r)) or SDDec(Mmin(r)) <= SDDec(r) & SDDec(
  r) < SDDec(M0(r))
proof
  let m,k be Nat;
  let r be Tuple of (m+2),k-SD;
  set MZero = SDDec(M0(r));
  set R = SDDec(r);
  assume that
A1: k >= 2;
  now
    per cases;
    suppose
      R < MZero;
      hence thesis by A1,Th4;
    end;
    suppose
      R >= MZero;
      hence thesis by A1,Th3;
    end;
  end;
  hence thesis;
end;
