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, a be non trivial Nat holds
   a |-count (a gcd b) = 0 iff not a |-count (a gcd b) = 1
   proof
     let b be non zero Nat, a be non trivial Nat;
     reconsider c = a gcd b as non zero Nat;
     a > 1 by Def0; then
     L1: a |-count (a gcd b) = 0 iff not a divides (a gcd b) by NAT_3:27;
     a gcd b divides b by INT_2:def 2;
     hence thesis by CD,INT_2:9,L1;
   end;
