reflexivity.
Qed.

(* Specifications: *)
Theorem PRF_NA_impl_NAI :
PRF_NAI_Advantage <= (maxLists / 1 * maxDistance)%rat.
Theorem IND_CPA_SecretKey_OI_G1_Hybrid :
Pr[IND_CPA_SecretKey_OI_G1] == Pr[ListHybrid_G _ A1 A3
(fun x =>
key <-$ KeyGen;
[b, _] <-$2 (A2 x) _ _ (EncryptNothingOracle _ ptDefault key) tt;
ret b
)].
Theorem G1_2_G1_equiv :
Pr[G1_2] == Pr[G1].
Theorem G2_3_bad_equiv :
Pr[x <-$ G2_3; ret (snd x)] == Pr[G2_3_bad].
Theorem hF_PRF :
PRF_Advantage ({0, 1}^(c + k)) ({0, 1}^c) hF _ _ A <=
PRF_Advantage ({0, 1}^c) ({0, 1}^c) h _ _ PRF_h_A +
Adv_WCR _ _ F (Rnd k) au_F_A.
Theorem G1_2_G1_equiv :
Pr[G1_2] == Pr[G1].
Theorem findCollision_1_correct :
forall (A B : Set) eqd1 eqd2 (ls : list (A * B)) (x1 x2 : A) y,
findCollision_1 eqd1 eqd2 ls x1 y =
Some x2 ->
x1 <> x2 /\
In (x2, y) ls.
Theorem hF_PRF :
PRF_Advantage ({0, 1}^(c + k)) ({0, 1}^c) hF _ _ A <=
PRF_Advantage ({0, 1}^c) ({0, 1}^c) h _ _ PRF_h_A +
Adv_WCR _ _ F (Rnd k) au_F_A.