Section AutIn.
Variable gT : finGroupType.
Definition Aut_in A (B : {set gT}) := 'N_A(B | 'P) / 'C_A(B | 'P).
Variables G H : {group gT}.
Hypothesis sHG: H \subset G.

Lemma restr_perm_Aut : restr_perm H @* Aut G \subset Aut H.