Definition ad_inj (pf:ad -> ad) :=
    forall a0 a1:ad, pf a0 = pf a1 -> a0 = a1.

Lemma ad_comp_double_plus_un_inj : forall pf:ad -> ad, ad_inj pf -> ad_inj (fun a0:ad => pf (Ndouble_plus_one a0)).