reserve G for Group,
  a,b for Element of G,
  m, n for Nat,
  p for Prime;

theorem
  for G being finite Group, H being Subgroup of G st
  G is p-group holds expon (H,p) <= expon (G,p)
proof
  let G be finite Group;
  let H be Subgroup of G;
  assume
A1: G is p-group;
  then card G = p |^ expon (G,p) by Def2;
  then ex r be Nat st
  card H = p |^ r & r <= expon (G,p) by Th2,GROUP_2:148;
  hence thesis by A1,Def2;
end;
