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 a be non trivial Nat, b,c be non zero Integer holds
  a|^(a |-count b) divides c & a|^(a |-count c) divides b
  implies a |-count b = a |-count c
  proof
    let a be non trivial Nat, b,c be non zero Integer;
    assume a|^(a |-count b) divides c & a|^(a |-count c) divides b;
    then a |-count b >= a |-count c & a |-count b <= a |-count c by DL;
    hence thesis by XXREAL_0:1;
  end;
