Contrasaturated sub-IAPS

Definition
Let $$(G,\Phi)$$ be an IAPS of groups and $$H$$ a sub-IAPS of $$G$$. We say that $$H$$ is contrasaturated inside $$G$$ if for any natural number $$n$$ and any $$g \in G_n$$, the following are true:


 * There exists a natural number $$n_1$$ and a $$g_1 \in G_{n_1}$$ such that $$\Phi_{n,n_1}(g,g_1) \in H_{n+n_1}$$
 * There exists a natural number $$n_2$$ and a $$g_2 \in G_{n_2}$$ such that $$\Phi_{n_2,n}(g_2,g) \in H_{n_2+n}$$

Another way of saying this is that the given sub-IAPS is not contained in any proper saturated sub-IAPS.