
theorem
  for m,k be Nat, r be Tuple of (m+2),k-SD st m >= 1 & k >= 2 holds
  SDDec(Mmask(r)) > 0 implies SDDec(r) > SDDec(M0(r))
proof
  let m,k be Nat, r be Tuple of (m+2),k-SD;
  assume that
A1: m >= 1 and
A2: k >= 2;
A3: m+2 > 1 by A1,Lm1;
  SDDec(M0(r)) + SDDec(Mmask(r)) = SDDec(r) + SDDec(DecSD(0,m+2,k)) by A2,Th17
    .= SDDec(r) + 0 by A3,RADIX_5:6;
  then
A4: SDDec(r) - SDDec(M0(r)) = SDDec(Mmask(r)) - 0;
  assume SDDec(Mmask(r)) > 0;
  hence thesis by A4,XREAL_1:47;
end;
