theorem Count7:
  for a,b be non trivial Nat, c be non zero Nat holds
    a|^((a |-count b)*(b |-count c)) <= c
  proof
    let a,b be non trivial Nat, c be non zero Nat;
    A1: a|^((a |-count b)*(b |-count c)) =
      (a|^(a |-count b))|^(b |-count c) by NEWTON:9;
    A2: (a|^(a |-count b))|^(b |-count c) <=
      b|^(b |-count c) by Count0,NEWTON02:41;
    b|^(b |-count c) <= c by Count0;
    hence thesis by A1,A2,XXREAL_0:2;
  end;
