reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for b be non zero Nat holds
  a > b implies ex p be prime Nat st p |-count a > p |-count b
  proof
    let b be non zero Nat;
    assume
    A1: a > b; then
    reconsider a as non zero Nat;
    (for p be prime Nat holds p|-count a <= p|-count b) implies a <= b
    proof
      assume for p be prime Nat holds p|-count a <= p |-count b; then
      for p be Element of NAT st p is prime holds
        p|-count a <= p |-count b; then
      consider c be Element of NAT such that
      B1: b = a*c by NAT_4:20;
      c is non zero by B1; then
      a*c >= a*1 by NAT_1:14,XREAL_1:64;
      hence thesis by B1;
    end;
    hence thesis by A1;
  end;
