reserve n for non zero Nat,
  j,k,l,m for Nat,
  g,h,i for Integer;

theorem
  j >= k implies MajP(m, j) >= MajP(m, k)
proof
  assume
A1: j >= k;
A2: MajP(m, j) >= m by Def1;
  2 to_power MajP(m, j) >= j by Def1;
  then 2 to_power MajP(m, j) >= k by A1,XXREAL_0:2;
  hence thesis by A2,Def1;
end;
