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 NAT328:
  for p be prime Nat, a,b be non zero Integer holds
    p |-count (a*b) = (p |-count a) + (p |-count b)
  proof
    let p be prime Nat, a,b be non zero Integer;
    reconsider k = |.a.|, l = |.b.| as non zero Nat;
    p |-count (a*b) = |.p.| |-count (|.a.|*|.b.|) by COMPLEX1:65
    .= |.p.| |-count k + |.p.| |-count l by NAT_3:28;
    hence thesis;
  end;
