reserve a,b,c for Integer;
reserve i,j,k,l for Nat;

theorem Th5:
  a = 0 & b = 0 iff a gcd b = 0
proof
  0 divides 0 gcd 0 by Def2;
  hence a = 0 & b = 0 implies a gcd b = 0;
  assume a gcd b = 0;
  then 0 divides a & 0 divides b by Def2;
  hence thesis;
end;
