Section RestrictActionTheory.
Variables (aT : finGroupType) (D : {set aT}) (rT : finType).
Variables (to : action D rT).

Lemma faithful_isom (A : {group aT}) S (nSA : actby_cond A S to) :
[faithful A, on S | to] -> isom A (actperm <[nSA]> @* A) (actperm <[nSA]>).